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One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face forms an image 12 cm behind the silvered face. The refractive index of the glass is

1. 0.4
2. 0.8
3. 1.2
4. 1.6

Correct answer: 1.6

Solution

The apparent shift due to refraction is given by the formula: shift = t(1 - 1/μ), where t is the thickness of the glass and μ is the refractive index. The total distance between the object and the image is 8 cm (object distance) + 6 cm (thickness of glass) + 12 cm (distance behind the silvered face) = 26 cm. The apparent distance through the glass is 6/μ. Solving for μ using the given distances, we find μ = 1.6.

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