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 :
(A)3.75 cm
(B)30 cm
(C)7.5 cm
(D)15 cm✓ Correct
Answer: (D)
Solution
For a concave mirror, magnification is
m=−uv
Given m=−3:
−3=−uv⟹v=3u
The object and image lie on the same side (both distances negative by convention), and the distance between them is 20 cm:
∣v−u∣=20
With u=−x and v=−3x (x > 0):
∣−3x−(−x)∣=2x=20⟹x=10
So u=−10cm, v=−30cm.
Using the mirror formula:
f1=v1+u1=−301+−101=−301−303=−304
f=−7.5cm
The radius of curvature:
R=2f=−15cm
The magnitude of the radius of curvature is 15cm.
JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Single correct option
