JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments
A prism of angle \(75^{\circ}\) and refractive index \(\sqrt{3}\) is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be ___________ .
\(\left(\sin 15^{\circ}=0.25\right.\) and \(\left.\sin 25^{\circ}=0.43\right)\)
- A between \(15^{\circ}\) and \(20^{\circ}\)
- B \(15^{\circ}\)
- C \(>25^{\circ}\)
- D \(<15^{\circ}\)
Answer & Solution
Correct Answer
(C) \(>25^{\circ}\)
Step-by-step Solution
Detailed explanation
\(r_1+r_2=75^{\circ}\) For T I R at back surface \(\sqrt{3} \sin r_2=\frac{3}{2} \sin 90^{\circ}\) \(r_2 \geq 60^{\circ}\) \(r_1 \leq 15^{\circ}\) \(1 \sin i=\sqrt{3} \sin 15^{\circ}\) \(\sin i =1.73 \times .25\) \(\sin i =.433\) \(i=25^{\circ} \Rightarrow i<25^{\circ}\)
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