Mirror Formula and Magnification Quiz
Magnification
Magnification (m) is a measure of how much larger or smaller an image is compared to the object. It is given by the ratio of the height of the image (hi) to the height of the object (ho).
Expression: m = hi / ho = -v / u
Cases of Magnification
- m > 1: The image is larger than the object.
- m < 1: The image is smaller than the object.
- m = 1: The image is the same size as the object.
- m > 0: The image is erect.
- m < 0: The image is inverted.
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.
Using the mirror formula: 1/f = 1/v + 1/u
1/10 = 1/v + 1/(-20)
1/v = 1/10 – 1/20 = 1/20
v = 20 cm (real, inverted)
2. An object is placed 30 cm in front of 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 = 1/15 – 1/30 = 1/30
v = 30 cm (virtual, erect)
3. An object is placed 10 cm from a concave mirror, and the image is formed at a distance of 30 cm from the mirror. Calculate the focal length of the mirror.
Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/(-30) + 1/(-10)
1/f = -1/30 – 1/10 = -4/30
f = -7.5 cm
4. Calculate the magnification of an object placed 25 cm from a concave mirror that forms an image at a distance of 50 cm.
Magnification (m) = -v/u
m = -50/(-25) = 2 (image is twice the size of the object)
5. An object 5 cm high is placed 20 cm in front of a convex mirror. The image is formed 10 cm behind the mirror. Calculate the height of the image.
Magnification (m) = v/u
m = -10/(-20) = 1/2
Height of image = m * height of object = 1/2 * 5 = 2.5 cm
6. An object is placed at the focal point of a concave mirror. Where is the image formed?
The image is formed at infinity.
7. Calculate the focal length of a concave mirror if an object placed at 15 cm from the mirror forms an image at 30 cm.
Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/(-30) + 1/(-15)
1/f = -1/30 – 1/15 = -3/30
f = -10 cm
8. An object is placed 25 cm in front of a convex mirror, forming an image 10 cm behind the mirror. Calculate the focal length of the mirror.
Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/(-10) + 1/(-25)
1/f = -1/10 – 1/25 = -7/50
f = -7.14 cm
9. An object is placed 40 cm from a concave mirror of focal length 20 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/20 = 1/v + 1/(-40)
1/v = 1/20 + 1/40 = 3/40
v = 40/3 cm = 13.33 cm (real, inverted)
10. An object is placed 10 cm from a convex mirror and the image is formed 5 cm behind the mirror. Calculate the focal length of the mirror.
Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/(-5) + 1/(-10)
1/f = -1/5 – 1/10 = -3/10
f = -3.33 cm
Medium Level Questions
11. An object is placed 60 cm from a concave mirror of focal length 30 cm. Calculate the image distance.
Using the mirror formula: 1/f = 1/v + 1/u
1/30 = 1/v + 1/(-60)
1/v = 1/30 + 1/60 = 3/60
v = 60/3 cm = 20 cm (real, inverted)
12. An object is placed 25 cm in front of a concave mirror of focal length 15 cm. Calculate the image distance and magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/15 = 1/v + 1/(-25)
1/v = 1/15 + 1/25 = 8/75
v = 75/8 cm = 9.375 cm (real, inverted)
Magnification (m) = -v/u
m = -9.375/(-25) = 0.375
13. An object is placed 50 cm from a convex mirror of focal length 20 cm. Calculate the image distance and magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/20 = 1/v + 1/(-50)
1/v = 1/20 – 1/50 = 3/100
v = 100/3 cm = 33.33 cm (virtual, erect)
Magnification (m) = v/u
m = -33.33/(-50) = 0.67
14. An object is placed 12 cm from a concave mirror of focal length 8 cm. Calculate the image distance and magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/8 = 1/v + 1/(-12)
1/v = 1/8 + 1/12 = 5/24
v = 24/5 cm = 4.8 cm (real, inverted)
Magnification (m) = -v/u
m = -4.8/(-12) = 0.4
15. An object is placed 10 cm from a convex mirror of focal length 5 cm. Calculate the image distance and magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/5 = 1/v + 1/(-10)
1/v = 1/5 – 1/10 = 1/10
v = 10 cm (virtual, erect)
Magnification (m) = v/u
m = -10/(-10) = 1
Hard Level Questions
16. Derive the mirror formula using ray diagrams for a concave mirror.
The derivation involves using the geometry of ray diagrams to show that 1/f = 1/v + 1/u.
17. What is the sign convention used for mirrors in ray diagrams?
The sign convention states that distances measured in the direction of the incident light are positive, and those measured against the direction are negative.
18. For a concave mirror, derive the relation between object distance, image distance, and focal length.
The relation is derived using similar triangles and the geometry of the mirror, resulting in the mirror formula: 1/f = 1/v + 1/u.
19. An object is placed 20 cm from a concave mirror, and the image is formed 40 cm from the mirror. Calculate the focal length of the mirror and the magnification.
Using the mirror formula: 1/f = 1/v + 1/u
1/f = 1/(-40) + 1/(-20)
1/f = -1/40 – 1/20 = -3/40
f = -13.33 cm
Magnification (m) = -v/u
m = -40/(-20) = 2
20. Compare and contrast the image formation by concave and convex mirrors, with examples.
Concave mirrors can produce real and virtual images depending on the object’s position, while convex mirrors always produce virtual, erect, and diminished images. For example, a concave mirror can focus light to a point, forming a real image, while a convex mirror is used for rearview mirrors in vehicles because it gives a wider field of view with virtual images.
