MHT CET · Physics · Ray Optics
A ray of light is incident at an angle 'i' on one face of a thin angled prism. The ray emerges normally from the other face. Refractive index of the glass prism is 'n' and
angle of prism is ' \(A^{\prime}\). The value of ' \(\mathrm{i}^{\prime}\) is
- A \(\mathrm{An}^{2}\)
- B \(\mathrm{~A}^{2} \mathrm{n}\)
- C \(\mathrm{An}\)
- D \(\frac{1}{\mathrm{An}}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{An}\)
Step-by-step Solution
Detailed explanation
(A)
For a prism \(\quad \mathrm{A}=\mathrm{r}_{1}+\mathrm{r}_{2}\)
here \(\quad r_{2}=0 \quad \therefore \quad A=r_{1}\)
Refractive index \(\mathrm{n}=\frac{\sin \mathrm{i}}{\sin \mathrm{r}_{1}}=\frac{\mathrm{i}}{\mathrm{r}_{1}}=\frac{\mathrm{i}}{\mathrm{A}}\)
\(\therefore \mathrm{i}=\mathrm{An}\)
For a prism \(\quad \mathrm{A}=\mathrm{r}_{1}+\mathrm{r}_{2}\)
here \(\quad r_{2}=0 \quad \therefore \quad A=r_{1}\)
Refractive index \(\mathrm{n}=\frac{\sin \mathrm{i}}{\sin \mathrm{r}_{1}}=\frac{\mathrm{i}}{\mathrm{r}_{1}}=\frac{\mathrm{i}}{\mathrm{A}}\)
\(\therefore \mathrm{i}=\mathrm{An}\)
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