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) $θ > \sin^{- 1} μ \sin A - \sin^{- 1} \frac{1}{μ}$

Show Answer

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,

$θ_{c} = \sin^{- 1} \frac{1}{μ}$

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

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

पिछला

अगला

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

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

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