Physics · Refraction of light at plane and spherical surfaces, thin lens formula and lens maker formula
An object is placed away from a convex lens of focal length and a sharp image is
An object is placed \( 30 \mathrm{cm} \) away from a convex lens of focal length \( 10 \mathrm{cm} \) and a sharp image is formed on a screen. Now a concave lens is placed in contact with the convex lens. The screen now has to be moved by \( 45 \mathrm{cm} \) to get a sharp image again. The magnitude of focal length of the concave len is (in cm)
- A. 72
- B. 60
- C. 36
- D. 20
Step-by-step solution
Using lens formula for convex lens: 1/v - 1/(-30) = 1/10 => v = 15 cm. After adding concave lens, screen moved by 45 cm so new image distance v' = 15 + 45 = 60 cm. Equivalent focal length F from 1/v' - 1/u = 1/F: 1/60 - 1/(-30) = 1/20 => F = 20 cm. For combination 1/F = 1/f1 + 1/f2: 1/20 = 1/10 + 1/f2 => f2 = -20 cm, magnitude 20 cm.
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