A ray of light is incident on a medium of refractive index ' μ ' at an angle of incidence ' i '. On refraction in the medium ' δ ' is the angle of deviation. Then (a) 1/μ = cos δ - (sin δ)/(tan i) (b) 1/μ = sin δ - (cos δ)/(tan i) (c) 1/μ = cos δ - sin δ · tan i. (d) 1/μ = sin δ - cos δ · tan i

Answer: (a). Deviation on refraction: δ = i - r ⇒ r = i - δ. 1/μ = (sin r)/(sin i) = (sin (i-δ))/(sin i) = (sin icos δ - cos isin δ)/(sin i). 1/μ = cos δ - (sin δ)/(tan i). So the answer is (a).

A ray of light is incident on a medium of refractive index ' μ ' at… | MHT CET 2024 (10 May, Shift 1)

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Refraction, Glass Slab & Apparent Depth

A ray of light is incident on a medium of refractive index ' $\mu$ ' at an angle of incidence ' $i$ '. On refraction in the medium ' $\delta$ ' is the angle of deviation. Then

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Answer: (a)

Deviation on refraction: $\delta = i - r \Rightarrow r = i - \delta$ .
$\dfrac{1}{\mu} = \dfrac{\sin r}{\sin i} = \dfrac{\sin(i-\delta)}{\sin i} = \dfrac{\sin i\cos\delta - \cos i\sin\delta}{\sin i}$ .
$\dfrac{1}{\mu} = \cos\delta - \dfrac{\sin\delta}{\tan i}$ .
So the answer is (a).

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