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Question
A ray of light incident at an angle θ on a refracting face of a prism emerges from the other face normally. If the angle of the prism is 5° and the prism is made of a material of refractive index 1.5, the angle of incidence is ______.
Options
7.5°
5°
15°
2.5°
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Solution
A ray of light incident at an angle θ on a refracting face of a prism emerges from the other face normally. If the angle of the prism is 5° and the prism is made of a material of refractive index 1.5, the angle of incidence is 7.5°.
Explanation:
In thin prisms, the distance between the refracting surfaces is ineligible and the angle of prism (A) is very small. Since A = r1 + r2, therefore if A is small then both r1 and r2 are also small, and the same is true for i1 and i2.
A = 5°
μ = 1.5
i2 = 0°
r2 = 0°
r1 + r2 = A
r1 = A - r2 = 5 – 0 = 5°
μ = `(sini1)/(sinrlμ) = (sinil)/(sinrl)`
⇒ `sini1 = μsinr1`
= `1.5 xx sin 5°`
= 1.5 xx 0.087`
= 0.1305
= 7.5°
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