Two glass prisms Pl and P2 are to be combined together to produce dispersion without deviation. The angle of the prisms P1 and P2 are selected as 40 and 30 respectively. If the refractive index of prism Pl is 1.54, then that of P2 will be:
Correct answer: D. 1.72
- A. 1.48
- B. 1.58
- C. 1.62
- D. 1.72
Explanation
To achieve dispersion without deviation when combining two prisms, the product of the refractive index and the angle of the prism must be equal for both prisms. Therefore, for prism P1 with an angle of 40° and a refractive index of 1.54, the product is 61.6. For prism P2, with an angle of 30°, the refractive index must be such that the product is the same, which means 30 * n = 61.6. Solving for n gives a refractive index of 1.72 for P2, making Option D correct. The other options do not satisfy this requirement due to their incorrect refractive index values.
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