Ray Optics and Optical Instruments · Question 60

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is -3, then the magnitude of the radius of curvature of the mirror is :

1. 3.75 cm
2. 15 cm
3. 7.5 cm
4. 30 cm

Answer

(2) 15 cm

Solution

m = - vu = -3 v = 3u (both on the object side, real image)

Let u = -x v = -3x

Distance between object and image: 3x - x = 20 x = 10 cm

u = -10 cm, v = -30 cm

1f = 1v + 1u = - 130 - 110 = - 430

f = -7.5 cm

|R| = 2|f| = 15 cm

Answer: (2)