/batch-001/55cde081adf2.webp" data-orsrc="https://uploads-pracbee-ramanuj.s3.ap-south-1.amazonaws.com/pyq-question-images/batch-001/55cde081adf2.webp" loading="lazy" style="max-width:100%;height:auto;display:block;margin:0 auto;max-height:40vh;vertical-align:baseline" alt="MHT CET 2025 26th April Morning Shift Physics - Ray Optics Question 22 English Explanation">According to given condition, the incident ray undergoes partial reflection and partial refraction at the face PR. Hence, applying Snell's law at face PR,

$$ \begin{aligned} & \mu \times \sin (A)=1 \times \sin (A+\delta) \\ \therefore \quad & \mu=\frac{\sin (A+\delta)}{\sin (A)} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)\end{aligned} $$

Similarly, at face PQ ,

$$ \mu \times \sin (2 A)=1 \times \sin (e) $$

$$ \therefore \quad \mu=\frac{\sin (e)}{\sin (2 A)} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(ii)$$

Equating equations (i) and (ii),

$$ \frac{\sin (A+\delta)}{\sin (A)}=\frac{\sin (e)}{\sin (2 A)} $$

However, for small angles, $\sin \theta \approx \theta$

$$ \begin{aligned} & \therefore \quad \frac{A+\delta}{A}=\frac{e}{2 A} \\ & \therefore \quad 2 A+2 \delta=e \\ & \therefore \quad A=\frac{e-2 \delta}{2} \end{aligned} $$

Given that, $\mathrm{e}=6.3^{\circ}$ and $\delta=1.15^{\circ}$

$$ \begin{aligned} &\therefore \quad \mathrm{A}=\frac{6.3-2(1.15)}{2}=2^{\circ}\\ &\text { Substituting the value in equation (i), }\\ &\mu=\frac{2+1.15}{2}=1.575 \end{aligned} $$

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