1. Define the principal focus of a concave mirror.
Ans. When a number of rays parallel to the principal axis are falling on a concave mirror, all meeting/intersecting at a point on the principal axis of the mirror. This point is called the principal focus of the concave mirror.
2. The radius of curvature of a spherical mirror is 20 cm. What is its focal length?
Ans. The radius of curvature is equal to twice the focal length. We put this as R = 2f .
Therefor focal length f = R/2 = 20/2 = 10 cm.
3. Name a mirror that can give an erect and enlarged image of an object.
Ans. A concave mirror can give an erect and enlarged image of an object when the object is kept between f and pole of the mirror.
4. Why do we prefer a convex mirror as a rear-view mirror in vehicles?
Ans. Convex mirrors are preferred as a rear-view mirror because they always give an erect, though diminished, image. Also, they have a wider field of view. Thus, convex mirrors enable the driver to view a much larger area than would be possible with a plane mirror.
5. Find the focal length of a convex mirror whose radius of curvature is 32 cm.
Ans. The radius of curvature is equal to twice the focal length. We put this as R = 2f.
Therefor focal length f = R/2 = 32/2 = 16 cm.
6. A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?
Ans. A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?
Ans. Solution: u = - 10 cm.
m = -3
v = ?
m = - v = - v
u -10
- 3 = -v
-10
v = - 30 cm.
v is negative means image is formed in the left side of the mirror.
(in front of a mirror).
7. A ray of light traveling in air enters obliquely into water. Does the light ray bend towards the normal or away from the normal? Why?
Ans. The speed of light is higher in a rarer medium than a denser medium. Thus, a ray of light when traveling from a rarer medium air to denser medium water slows down and bends towards the normal.
8. Light enters from air to glass having a refractive index 1.50. What is the speed of light in the glass? The speed of light in a vacuum is 3 × 10^8 m/s.
Ans. We know that refractive index =
Speed of light in air
Speed of light in a medium
Therefore the speed of light in glass
= speed of light in air
Refractive index
= 3 x 10^8
1.50
= 2 x 10^8 m /s.
9. You are given kerosene, turpentine, and water. In which of these does the light travel fastest?
Ans. Medium with the larger refractive index is an optically denser medium. The medium of lower refractive index is optically rarer. The speed of light is higher in a rarer medium than a denser medium.
Here the refractive index of - kerosene is 1.44, turpentine is 1.47 and water is 1.33. The Refractive index of water is lower so the light travels fastest in water.
10. Define 1 dioptre of power of a lens.
Ans. 1 dioptre is the power of a lens whose focal length is 1 meter.
1D = 1m^–1.
The power of a convex lens is positive and that of a concave lens is negative.
Ans. The needle should be placed at the C center of curvature to get an image of equal size. Therefore if image distance is 50 cm then object distance will be 50 cm.
12. Find the power of a concave lens of focal length 2 m.
Ans. We have power P = 1/f = 1/2 = 0.5D
13. Which one of the following materials cannot be used to make a lens?
(a) Water (b) Glass (c) Plastic (d) Clay
Ans. (d) Clay is not an optical medium.
14. The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object?
(a) Between the principal focus and the center of curvature
(b) At the center of curvature
(c) Beyond the center of curvature
(d) Between the pole of the mirror and its principal focus.
Ans. (d) Between the pole of the mirror and its principal focus.
15. Where should an object be placed in front of a convex lens to get a real image of the size of the object?
(a) At the principal focus of the lens
(b) At twice the focal length
(c) At infinity
(d) Between the optical center of the lens and its principal focus.
Ans. (b) At twice the focal length
16. A spherical mirror and a thin spherical lens have each a focal length of –15 cm. The mirror and the lens are likely to be
(a) both concave.
(b) both convex.
(c) the mirror is concave and the lens is convex.
(d) the mirror is convex, but the lens is concave.
Ans. (a) both concave.
17. No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be (a) plane. (b) concave. (c) convex. (d) either plane or convex.
Ans. (a) plane.
18. Which of the following lenses would you prefer to use while reading small letters found in a dictionary?
(a) A convex lens of focal length 50 cm.
(b) A concave lens of focal length 50 cm.
(c) A convex lens of focal length 5 cm.
(d) A concave lens of focal length 5 cm.
Ans. (a) A convex lens of focal length 50 cm.
19. Name the type of mirror used in the following situations.
(a) Headlights of a car.
(b) Side/rear-view mirror of a vehicle.
(c) Solar furnace. Support your answer with reason.
Ans. (a) Concave mirror.
(b) Convex mirror.
(c) Concave mirror.
20. One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations.
Ans. Yes, this lens will produce a complete image of the object. A large number of rays emanating from a point could be considered. However, it is more convenient to consider only two rays, for the sake of clarity of the ray diagram. However, the brightness of the image will reduce.
21. An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and nature of the image formed.
Ans. We have height of object h = 5 cm
object distance from lens u = -25 cm
focal length f= - 10 cm
1/v = 1/f + 1/u = 1/10 + 1/-25
= 1/10 - 1/25 = (5 - 2)/50 = 3/50
1/v = 3/50
Image distance v = 50/3 = 16.67 or nearly 17 cm
height of image h' = (-v x h)/u = (-17 x 5)/ -25 = 3.4 cm
22. A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens?
Ans. We have
Image distance from lens v = -10 cm
focal length f= - 15 cm
1/u = 1/v - 1/f = 1/-10 + 1/-15
= 1/-10 - 1/-15 = 1/15 - 1/10 = (2 - 3)/30 = -1/30
1/u = -1/30
Object distance u = - 30cm.
Thus the object is placed 30 cm away from the concave lens. The negative sign shows that the object is at 30cm in front of the lens.
23. An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.
Ans. Given u = -10 cm, f= +15 cm
We have 1/f = 1/v + 1/u
1/v = 1/f - 1/u = 1/15 - 1/-10 = 1/15 + 1/10
1/v = (2+3)/30 = 5/30
v = + 6 cm.(+ means virtual)
Position of Image : Behind the mirror between f and pole.
Nature of image: Erect, diminished and virtual.
24. The magnification produced by a plane mirror is +1. What does this mean?
Ans. The magnification produced by a plane mirror is +1 means, an image formed by the mirror is virtual, erect and size of the image is equal to the size of the object.
25. An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature, and its size.
Ans. Here given height (h) = 5 cm, u = -20 cm
f = +15 cm ( f=1/2 C)
1/f = 1/v + 1/u
1/v = 1/f - 1/u = 1/15 - 1/-20 = (4 + 3)/60
1/v = 7/60
v = 60/7 = 8.77 cm= nearly 9 cm.
height of image h'=-v/u x h = 9x5/-20 = -9/4 = -2.25cm.
Position of image: Behind the mirror between f and p.
Nature: Virtual
Size: Diminished
26. An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed so that a sharply focused image can be obtained? Find the size and nature of the image.
Ans. Solution Object-size, h = + 7 cm;
Object-distance, u = – 27 cm;
Focal length, f = –18 cm;
Image-distance, v = ?
Image-size, h′ = ?
1 = 1 - 1 = 1 - 1 = - 1 + 1 = -3 + 2 = -1
v f u -18 -27 18 27 54 54
v = – 54 cm The screen should be placed at 54 cm from the mirror. The image is real.
m = h'/h = h'/7
m = h'/h = -v/u
h' = -v/u x h = 54/27 x 7 = 2 x 7 = -14cm.
Also, magnification, m = Height of the image, h′ = – 14 cm The image is inverted and enlarged.
27. Find the focal length of a lens of power – 2.0 D. What type of lens is this?
Ans. We know that power P = 1/f in m.
- 2 D = 1/ f
f = - 1/2 m
f = - 50 cm.
The lens is concave.
28. A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?
Ans. We know that power = 1/f in m.
+ 1.5 = 1/ f
f = 1/1.5 m = 1000/15 = 66.6 cm
Lens is converging.
Additional Questions
1. What do you understand by regular and defused reflection?
Ans. When the parallel rays of light coming from the same direction and incident on a smooth polished surface, then all incident rays reflect in the same direction in a parallel way. This is called regular reflection If the surface is rough, then the parallel rays will reflect in many different directions, in what is called diffuse reflection.
2. What is a lateral inversion?
Ans. The phenomenon due to which the left-hand side of an object appears as the right-hand side of the object and vice versa is called lateral inversion.
3. What does m = +1 stand for?
Ans. m = +1 stand for, the magnification produced by a plane mirror is +1.
Positive(+1) indicates an image formed by the mirror is virtual, erect and size of the image is equal to the size of the object.
4. What is the focal length of a plane mirror?
Ans. The focal length of the plane mirror is infinity.
Reason - If a plain mirror can be considered as the spherical mirror of an infinite radius of curvature then the focal length will be infinite.
5. Define the refraction of light.
Ans. When light traveling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as the refraction of light.
6. Name the type of mirror which always forms a virtual and diminished image.
Ans. Convex mirror.
7. What Sign is given to the focal length of a concave mirror and convex mirror?
Ans. The negative focal length of a concave mirror and positive focal length of the convex mirror.
8. In which of the following media glass, water, and diamond
(a) light travels fastest
(b) light travels slowest.
Ans. (a) Diamond most optically denser medium and have the largest refractive index. Hence light travels fastest in a diamond.
(b) Water is the most optically rarer medium and has a less refractive index. Hence light travels slowest in water.
9. State the relation between object distance, image distance and focal length of a spherical mirror.
Ans. 1 = 1 + 1
f u v
Here f= focal length, v = image distance and u = object distance.
10. A 10 mm long nail is placed vertically in front of a concave mirror. A 5 mm long image of the nail is formed at 30 cm in front of the mirror. What is the focal length of this?
Ans. Here given: height of the object h = 10 mm = 1 cm.
height of the image h' = -5 mm = 0.5 cm
image distance v = - 30 cm.
We have m = h'/h = -v/u
-0.5/ 1 = - (-30) / u
u = 30/-0.5 = -300/5=-60 cm.
We know that 1/f = 1/v + 1/u= 1/-30 + 1/-60
1/ f = (-2 - 1)/60 = -3/60 = -1/20
1/f = -1/20
f = - 20 cm.
11. Under which conditions, a concave mirror can form an image larger than the actual object?
Ans. When the parallel rays of light coming from the same direction and incident on a smooth polished surface, then all incident rays reflect in the same direction in a parallel way. This is called regular reflection If the surface is rough, then the parallel rays will reflect in many different directions, in what is called diffuse reflection.
2. What is a lateral inversion?
Ans. The phenomenon due to which the left-hand side of an object appears as the right-hand side of the object and vice versa is called lateral inversion.
3. What does m = +1 stand for?
Ans. m = +1 stand for, the magnification produced by a plane mirror is +1.
Positive(+1) indicates an image formed by the mirror is virtual, erect and size of the image is equal to the size of the object.
4. What is the focal length of a plane mirror?
Ans. The focal length of the plane mirror is infinity.
Reason - If a plain mirror can be considered as the spherical mirror of an infinite radius of curvature then the focal length will be infinite.
5. Define the refraction of light.
Ans. When light traveling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as the refraction of light.
6. Name the type of mirror which always forms a virtual and diminished image.
Ans. Convex mirror.
7. What Sign is given to the focal length of a concave mirror and convex mirror?
Ans. The negative focal length of a concave mirror and positive focal length of the convex mirror.
8. In which of the following media glass, water, and diamond
(a) light travels fastest
(b) light travels slowest.
Ans. (a) Diamond most optically denser medium and have the largest refractive index. Hence light travels fastest in a diamond.
(b) Water is the most optically rarer medium and has a less refractive index. Hence light travels slowest in water.
9. State the relation between object distance, image distance and focal length of a spherical mirror.
Ans. 1 = 1 + 1
f u v
Here f= focal length, v = image distance and u = object distance.
10. A 10 mm long nail is placed vertically in front of a concave mirror. A 5 mm long image of the nail is formed at 30 cm in front of the mirror. What is the focal length of this?
Ans. Here given: height of the object h = 10 mm = 1 cm.
height of the image h' = -5 mm = 0.5 cm
image distance v = - 30 cm.
We have m = h'/h = -v/u
-0.5/ 1 = - (-30) / u
u = 30/-0.5 = -300/5=-60 cm.
We know that 1/f = 1/v + 1/u= 1/-30 + 1/-60
1/ f = (-2 - 1)/60 = -3/60 = -1/20
1/f = -1/20
f = - 20 cm.
11. Under which conditions, a concave mirror can form an image larger than the actual object?
Ans. If we place an object less then 2f from a concave mirror, then the image will be larger than the object.
12. What is the minimum distance between an object and its real image in the case of the concave mirror?
Ans. The minimum distance is zero because when the object is at the center of curvature, the image will be also formed at C of equal size.
13. Rays from sun converge at a point 15 cm in front of a concave mirror. Where should an object be placed so that the size of its image is equal to the size of the object?
13. Rays from sun converge at a point 15 cm in front of a concave mirror. Where should an object be placed so that the size of its image is equal to the size of the object?
Ans. The focal length of a concave mirror is 15 cm. Therefore the radius of curvature will be 30 cm. The object should be placed at C, 30 cm in front of a concave mirror so that the size of its image is equal to the size of the object.
14. In which of these media the Ray of light incident obliquely at the same angle would bend most? Water, mustard oil, glycerine, and kerosene.
Ans. Glycerine is the most optically denser medium and has the largest refractive index. Hence glycerine would bend most.
15. What is the unit of the refractive index?
Ans. The Refractive index has no refractive index because it is a ratio.
16. The refractive index of diamond is 2.42. What is the meaning of this statement?
Ans. The meaning of this statement is that the speed of light in air is 2.24 times the speed of light in a diamond.
Or the ratio of the speed of light in air to the speed of light in the diamond is 2.42.
17. Why is the refractive index of the atmosphere different at different altitudes?
Ans. The Refractive index is of atmosphere different at different altitudes due to different density of atmosphere above the earth.
18. What is the difference between virtual images and real images?
Ans. The real image is obtained when a ray of light after reflection actually converges at a point. It can be obtained on the screen and can be seen with the eye.
A virtual image formed when rays of light do not actually meet but appear to meet when produced backward. It cannot be obtained on the screen.
15. What is the unit of the refractive index?
Ans. The Refractive index has no refractive index because it is a ratio.
16. The refractive index of diamond is 2.42. What is the meaning of this statement?
Ans. The meaning of this statement is that the speed of light in air is 2.24 times the speed of light in a diamond.
Or the ratio of the speed of light in air to the speed of light in the diamond is 2.42.
17. Why is the refractive index of the atmosphere different at different altitudes?
Ans. The Refractive index is of atmosphere different at different altitudes due to different density of atmosphere above the earth.
Ans. The real image is obtained when a ray of light after reflection actually converges at a point. It can be obtained on the screen and can be seen with the eye.
A virtual image formed when rays of light do not actually meet but appear to meet when produced backward. It cannot be obtained on the screen.
19. What are the three factors on which the lateral displacement of an emergent ray from a glass lab depends?
Ans. The lateral displacement depends on:
(a) the thickness of the glass
(b) the angle of incidence and
(c) the refractive index of glass
Ans. The lateral displacement depends on:
(a) the thickness of the glass
(b) the angle of incidence and
(c) the refractive index of glass
20. What makes things visible?
Ans. An object reflects light that falls on it and this reflected light, when received by our eyes, we can see things.
21. What kind of mirror is used in a solar furnace? Give a reason for using this mirror.
32. Where the bulb is placed in torch, searchlights, and headlights of vehicles?
33. Arrange the following common substances in the increasing order of refractive indices Ice, Kerosene, Glass, Diamond, Alcohol, Water
21. What kind of mirror is used in a solar furnace? Give a reason for using this mirror.
Ans. A large concave mirror is used in a solar furnace to concentrate sunlight to produce heat in solar furnaces.
22. What is the range of wavelengths of visible light?
Ans. The range of wavelengths of visible light is between 700 nm to 400 nm.
23. When a light ray passes obliquely to the atmosphere in an upward direction, how does its path generally change?
Ans. When a light ray passes obliquely to the atmosphere in an upward direction, due to atmospheric refraction its path changes. The atmospheric layer has a different optical density so refraction takes place.
24. Why are convex mirror preferred over plane mirrors as rearview mirrors in vehicles?
31. Why does the pool or a bottom of a tank containing water appear to be raised?
22. What is the range of wavelengths of visible light?
Ans. The range of wavelengths of visible light is between 700 nm to 400 nm.
23. When a light ray passes obliquely to the atmosphere in an upward direction, how does its path generally change?
Ans. When a light ray passes obliquely to the atmosphere in an upward direction, due to atmospheric refraction its path changes. The atmospheric layer has a different optical density so refraction takes place.
23. When a light ray passes obliquely to the atmosphere in an upward direction, how does its path generally change?
Ans. When a light ray passes obliquely to the atmosphere in an upward direction, due to atmospheric refraction its path changes. An atmospheric layer has a different optical density so refraction takes place.
Ans. When a light ray passes obliquely to the atmosphere in an upward direction, due to atmospheric refraction its path changes. An atmospheric layer has a different optical density so refraction takes place.
Ans. Convex mirrors are preferred as a rear-view mirror because they always give an erect, though diminished, image. Also, they have a wider field of view. Thus, convex mirrors enable the driver to view a much larger area than would be possible with a plane mirror.
25. What is the change in the image observed as the object is moved from Infinity towards the concave lens?
Ans. The image grows in size and remains inverted.
Ans. The image grows in size and remains inverted.
26. What are the values of angle of incidence 'i' and the angle of reflection 'r' for a normal incidence?
Ans. The angle of incidence 'i' and the angle of reflection 'r' for a normal incidence will be zero.
Ans. The angle of incidence 'i' and the angle of reflection 'r' for a normal incidence will be zero.
27. How does the size of the image change as the object is brought closer from infinity towards the convex lens?
Ans. The size of the image increases as the object is brought closer from infinity towards the focus of the convex lens.
Ans. The size of the image increases as the object is brought closer from infinity towards the focus of the convex lens.
28. Does the speed of light increases or decreases in a medium in comparison to its value in a vacuum?
Ans. It decreases always because light travels faster in a vacuum.
Ans. It decreases always because light travels faster in a vacuum.
29. Name a mirror that can give an erect and enlarged image of an object.
Ans. A concave mirror can give an erect and enlarged image of an object when an object is kept between f and pole of the mirror.
30. Do all Cartesian signs applicable in each case of a spherical lens as in the mirror?
Ans. Yes.
Ans. A concave mirror can give an erect and enlarged image of an object when an object is kept between f and pole of the mirror.
Ans. Yes.
Ans. The pool or a bottom of a tank containing water appears to be raised due to the refraction of light.
32. Where the bulb is placed in torch, searchlights, and headlights of vehicles?
Ans. At focus or very near the focus, the bulb is placed to get parallel beams of light and to focus the light at the longer distances.
33. Arrange the following common substances in the increasing order of refractive indices Ice, Kerosene, Glass, Diamond, Alcohol, Water
Ans. Ice, Water, Alcohol, Kerosene, Glass, Diamond.
34. Define the reflection of light.
Ans. When a ray of light falls on a highly polished surface, such as a mirror, it bounces back in the same medium is called the reflection of light?
Ans. When a ray of light falls on a highly polished surface, such as a mirror, it bounces back in the same medium is called the reflection of light?
35. Define optical density.
Ans. The ability of a medium to refract light is also expressed in terms of its optical density. Optical density has a definite connotation.
36. Find the power of a concave lens of focal length 2 m.
Ans. We know that power = 1/f in m.
= 1/ 2
= - 0.5 D
37. A spherical mirror and a thin spherical lens have each a focal length of –15 cm. What type of mirror and lens are these?
Ans. Both are concave.
38. No matter how far you stand from a mirror, your image appears erect. What type of mirror and lens are these.
Ans. Either plain mirror or convex mirror or concave lens.
39. Which type of lenses would you prefer to use while reading small letters found in a dictionary? Convex with 50 cm focus or convex with 5 cm focus?
Ans. A convex lens of the focal length of 50 cm. Because when an object is placed between the pole and focal point, we will get an enlarged and erect image of letters of the dictionary.
40. What Sign is given to the focal length of a concave mirror and convex mirror?
Ans. The negative focal length of a concave mirror and positive focal length of the convex mirror.
Ans. The negative focal length of a concave mirror and positive focal length of the convex mirror.
41. What is the relationship between the radius of curvature R, and focal length f, of a spherical mirror?
Ans. For spherical mirrors of small apertures, the radius of curvature is found to be equal to twice the focal length.
R = 2f .
42. What is the cause of refraction?
Ans. Refraction is due to a change in the speed of light as it enters from one transparent medium to another.
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