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A plano-convex lens of glass (refractive index 1.5) has its convex…
Question
A plano-convex lens of glass (refractive index 1.5) has its convex surface (radius of curvature 20 cm) silvered, while the flat surface faces the incoming light. Light enters through the flat face, refracts at the convex glass surface, reflects off the silvered convex surface, and refracts back out. Find the magnitude of the focal length (in cm) of the equivalent mirror.
✓ Verified answer: 6.666667checked by our engine — not a guess
Step-by-step solution
Lens power: 1/f = (n-1)/R = 0.5/20 = 1/40, P_L = 1/40.
The silvered convex surface acts as a concave mirror of focal length R/2 = 10 cm, power P_m = 1/10.
Equivalent mirror power P = 2P_L + P_m = 2/40 + 1/10 = 1/20 + 2/20 = 3/20.
Focal length = 20/3 = 6.667 cm.
Final answer6.667
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