SATHEE: Optics 4 Question 5

Optics 4 Question 5

5. Monochromatic light is incident on a glass prism of angle $A$ . If the refractive index of the material of the prism is $μ$ , a ray incident at an angle $θ$ , on the face $A B$ would get transmitted through the face $A C$ of the prism provided

(2015 Main)

(a) $θ < \cos^{- 1} [μ \sin (A + \sin^{- 1} (\frac{1}{μ}))]$

(b) $θ < \sin^{- 1} [μ \sin (A - \sin^{- 1} (\frac{1}{μ}))]$

(d) $θ > \sin^{- 1} [μ \sin (A - \sin^{- 1} (\frac{1}{μ}))]$

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Answer:

Correct Answer: 5. (d)

Solution:

Applying Snell’s law at $M$ ,

$\begin{matrix} μ = \frac{\sin θ}{\sin r_{1}} \\ ∴ r_{1} = \sin^{- 1} (\frac{\sin θ}{μ} or \sin r_{1} = \frac{\sin θ}{μ}) \end{matrix}$

Now, $r_{2} = A - r_{1} = A - \sin^{- 1} (\frac{\sin θ}{μ})$

Ray of light would get transmitted form face $A C$ if

$r_{2} < θ_{c} or A - \sin^{- 1} (\frac{\sin θ}{μ}) < θ_{c}$

where,

$θ_{c} = \sin^{- 1} (\frac{1}{μ})$

$∴ \sin^{- 1} (\frac{\sin θ}{μ} > A - θ_{c})$

$\begin{aligned} or & (\frac{\sin θ}{μ}) > \sin (A - θ_{c}) \\ ∴ & θ > \sin^{- 1} [μ \sin (A - θ_{c})] \\ or & θ > \sin^{- 1} [μ \sin (A - \sin^{- 1} (\frac{1}{μ}))] \end{aligned}$

Optics 4 Question 5

5. Monochromatic light is incident on a glass prism of angle $A$ . If the refractive index of the material of the prism is $μ$ , a ray incident at an angle $θ$ , on the face $A B$ would get transmitted through the face $A C$ of the prism provided

Answer:

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Optics 4 Question 5

5. Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ, a ray incident at an angle θ, on the face AB would get transmitted through the face AC of the prism provided

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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5. Monochromatic light is incident on a glass prism of angle $A$ . If the refractive index of the material of the prism is $μ$ , a ray incident at an angle $θ$ , on the face $A B$ would get transmitted through the face $A C$ of the prism provided