Most Important Numericals of Mirror Formula of Light Chapter Class 10th With Explanation that are beneficial for the various board exams.
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Easy Level Questions
1. An object is placed 20 cm from a concave mirror with a focal length of 10 cm. Calculate the image distance and the magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/-10 = 1/v + 1/-20
1/v = -1/20
v = -20 cm (real, inverted)
Magnification (m) = -v/u = -(-20)/(-20) = -1 (image is the same size as the object)
2. An object is placed 30 cm from a convex mirror with a focal length of 15 cm. Calculate the image distance and the magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/15 = 1/v + 1/-30
1/v = 3/30
v = +10 cm (virtual, upright)
Magnification (m) = -v/u = -10/-30 =+ 1 /3 (image is the smaller than the size as the object)
3. An object is placed 25 cm from a concave mirror and the image is formed at 50 cm from the mirror. Calculate the focal length of the mirror.
Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/(-50) + 1/(-25)
1/f = -3/50
f = -16.67 cm (concave mirror)
4. An object is placed 60 cm from a convex mirror and the image is formed at 24 cm from the mirror. Calculate the focal length and the magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/24 + 1/(-60)
1/f = 3/120
f = +40 cm (convex mirror)
Magnification (m) = -v/u = -24/-60 = +0.4
5. An object is placed 15 cm from a concave mirror with a focal length of 10 cm. Calculate the image distance and the magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/-10 = 1/v + 1/-15
1/v = -1/30
v = -30 cm (real, inverted)
Magnification (m) = -v/u = -(-30)/(-15) = -2 (image is twice the size of the object)
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Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/40 + 1/(-80)
1/f = 1/80
f = 80 cm (convex mirror)
7. A concave mirror produces a real image 3 times the size of the object. If the focal length is 20 cm, find the object distance.
Using the magnification formula: m = -v/u = 3
v = 3u
Using the mirror formula: 1/f = 1/v + 1/u
1/(-20) = 1/(3u) + 1/u
u = -26.67 cm
8. A convex mirror produces an image that is one-third the size of the object. If the focal length is 30 cm, find the object distance.
Using the magnification formula: m = -v/u = 1/3
v = -u/3
Using the mirror formula: 1/f = 1/v + 1/u
1/30 = 1/-(u/3) + 1/u
u = -60 cm
9. An object is placed 10 cm from a concave mirror with a focal length of 15 cm. Calculate the image distance and the magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/-15 = 1/v + 1/(-10)
1/v = 1/30
v = +30 cm (virtual, erect)
Magnification (m) = -v/u = -(30)/(-10) = +3 (image is three times the size of the object)
10. A convex mirror with a focal length of 20 cm produces an image that is half the size of the object. Calculate the object distance.
Using the magnification formula: m = -v/u = 1/2
v = -u/2
Using the mirror formula: 1/f = 1/v + 1/u
1/20 = 1/-(u/2) + 1/u
u = -20 cm
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Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/(-75) + 1/(-25)
1/f = -4/75
f = -18.75 cm (concave mirror)
12. An object is placed 100 cm from a convex mirror with a focal length of 50 cm. Calculate the image distance and the magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/50 = 1/v + 1/(-100)
1/v = 3/100
v = +33.3 cm (virtual, upright)
Magnification (m) = -v/u = -33.3/-100 = +0.33 (image is smaller than the size as the object)
13. An object is placed 35 cm from a concave mirror with a focal length of 20 cm. Calculate the image distance and the magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/-20 = 1/v + 1/-35
1/v = -3/140
v = -46.6 cm (real, inverted)
Magnification (m) = -v/u = -(-46.6)/(-35) = -1.4 (image is greater than the size as the object)
14. An object is placed 55 cm from a convex mirror with a focal length of 30 cm. Calculate the image distance and the magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/30 = 1/v + 1/-55
1/v = 1/55
v = 55 cm (virtual, upright)
Magnification (m) = -v/u = 55/-55 = -1 (image is the same size as the object)
15. An object is placed 30 cm from a concave mirror with a focal length of 20 cm. If the height of the object is 5 cm, calculate the height of the image.
Using the mirror formula: 1/f = 1/v + 1/u
1/-20 = 1/v + 1/(-30)
1/v = -1/60
v = -60 cm (real, inverted)
Magnification (m) = -v/u = -(-60)/(-30) = 2
Height of image = m × height of object = 2 × 5 cm = 10 cm (inverted)
16. A 4 cm tall object is placed 25 cm from a concave mirror with a focal length of 15 cm. Calculate the height of the image.
Using the mirror formula: 1/f = 1/v + 1/u
1/-15 = 1/v + 1/(-25)
1/v = -2/75
v = -37.5 cm (real, inverted)
Magnification (m) = -v/u = -(-37.5)/(-25) = -1.5
Height of image = m × height of object = -1.5 × 4 cm = -6 cm (inverted)
17. A concave mirror produces a virtual image that is three times the height of a 2 cm tall object. If the focal length of the mirror is 10 cm, calculate the object distance.
Using the magnification formula: m = -v/u = 3
v = 3u
Using the mirror formula: 1/f = 1/v + 1/u
1/-10 = 1/(3u) + 1/u
u = -7.5 cm (object should be placed 7.5 cm from the mirror)
18. An object is placed 50 cm from a concave mirror and the height of the image is 4 times the height of the object. If the focal length is 25 cm, calculate the height of the image.
Using the magnification formula: m = -v/u = 4
v = 4u
Using the mirror formula: 1/f = 1/v + 1/u
1/-25 = 1/(4u) + 1/u
u = -66.67 cm
v = -266.67 cm (real, inverted)
Height of image = 4 × height of object
19. A 5 cm tall object is placed 40 cm from a concave mirror with a focal length of 20 cm. Calculate the image distance and the height of the image.
Using the mirror formula: 1/f = 1/v + 1/u
1/-20 = 1/v + 1/(-40)
1/v = -1/40
v = -40 cm (real, inverted)
Magnification (m) = -v/u = -(-40)/(-40) = 1
Height of image = m × height of object = 1 × 5 cm = 5 cm (inverted)
20. An object is placed 15 cm from a concave mirror, and the image formed is twice the height of the object. If the focal length is 10 cm, calculate the image distance and the height of the image.
Using the magnification formula: m = -v/u = 2
v = 2u
Using the mirror formula: 1/f = 1/v + 1/u
1/-10 = 1/(2u) + 1/u
u = -7.5 cm
v = -15 cm (real, inverted)
Height of image = 2 × height of object
21. A concave mirror produces a real image that is 5 cm tall when a 2 cm tall object is placed 10 cm from the mirror. Calculate the magnification and the focal length of the mirror.
Using the magnification formula: m = height of image / height of object = 5/2 = 2.5
m = -v/u
Using the mirror formula: 1/f = 1/v + 1/u
u = -10 cm
v = 2.5u = -25 cm
1/f = 1/(-25) + 1/(-10)
f = -7.14 cm (concave mirror)
22. An object is placed 75 cm from a concave mirror with a focal length of 25 cm. If the height of the image is 1.5 times the height of the object, calculate the height of the image.
Using the mirror formula: 1/f = 1/v + 1/u
1/-25 = 1/v + 1/(-75)
1/v = -2/75
v = -37.5 cm (real, inverted)
Magnification (m) = -v/u = -(-37.5)/(-75) = 0.5
Height of image = 1.5 × height of object
23. A 3 cm tall object is placed 18 cm from a concave mirror with a focal length of 12 cm. Calculate the image distance and the height of the image.
Using the mirror formula: 1/f = 1/v + 1/u
1/-12 = 1/v + 1/(-18)
1/v = -1/36
v = -36 cm (real, inverted)
Magnification (m) = -v/u = -(-36)/(-18) = 2
Height of image = 2 × 3 cm = 6 cm (inverted)
24. A 4 cm tall object is placed 50 cm from a concave mirror. The image formed is twice the height of the object. Calculate the focal length of the mirror and the height of the image.
Using the magnification formula: m = -v/u = 2
v = 2u
Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/(2u) + 1/u
f = -33.33 cm (concave mirror)
Height of image = 2 × 4 cm = 8 cm (inverted)
25. An object is placed 30 cm from a convex mirror with a focal length of 15 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/15 = 1/v + 1/-30
1/v = 3/30
v = +10 cm (virtual, upright)
26. An object is placed 10 cm from a concave mirror with a focal length of 5 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/-5 = 1/v + 1/-10
1/v = -1/10
v = -10 cm (real, inverted)
27. An object is placed 100 cm from a convex mirror with a focal length of 50 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/50 = 1/v + 1/-100
1/v = 3/100
v = +33.3 cm (virtual, upright)
28. An object is placed 150 cm from a concave mirror with a focal length of 75 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/-75 = 1/v + 1/-150
1/v = -1/150
v = -150 cm (real, inverted)
29. An object is placed 45 cm from a convex mirror with a focal length of 30 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/30 = 1/v + 1/-45
1/v = 5/90
v = +18 cm (virtual, upright)
30. An object is placed 20 cm from a concave mirror with a focal length of 10 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/-10 = 1/v + 1/-20
1/v = -1/20
v = -20 cm (real, inverted)
31. An object is placed 35 cm from a convex mirror with a focal length of 20 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/20 = 1/v + 1/-35
1/v = 11/140
v = +12.7 cm (virtual, upright)
32. An object is placed 75 cm from a concave mirror with a focal length of 25 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/-25 = 1/v + 1/-75
1/v = -2/75
v = -37.5 cm (real, inverted)
33. An object is placed 40 cm from a convex mirror with a focal length of 20 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/20 = 1/v + 1/-40
1/v = 3/40
v = +13.3 cm (virtual, upright)
34. An object is placed 90 cm from a concave mirror with a focal length of 30 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/-30 = 1/v + 1/-90
1/v = -2/90
v = -45 cm (real, inverted)
35. An object is placed 22 cm from a convex mirror with a focal length of 11 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/11 = 1/v + 1/-22
1/v = 3/22
v = +7.33 cm (virtual, upright)
36. An object is placed 200 cm from a concave mirror with a focal length of 100 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/-100 = 1/v + 1/-200
1/v = -1/200
v = -200 cm (real, inverted)
37. An object is placed 120 cm from a convex mirror with a focal length of 60 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/60 = 1/v + 1/-120
1/v = 3/120
v = +40 cm (virtual, upright)
38. An object is placed 250 cm from a concave mirror with a focal length of 125 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/-125 = 1/v + 1/-250
1/v = -1/250
v = -250 cm (real, inverted)
39. An object is placed 60 cm from a convex mirror with a focal length of 30 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/30 = 1/v + 1/-60
1/v = 3/60
v = +20 cm (virtual, upright)
40. An object is placed 60 cm from a concave mirror with a focal length of 20 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/-20 = 1/v + 1/-60
1/v = -2/30
v = -15 cm (real, inverted)
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