SATHEE: ray-optics-and-optical-instruments Question 33

किरण प्रकाशिकी और ऑप्टिकल उपकरण

Question: Q. 10. A ray of light, incident on an equilateral glass prism $(μ_{g} = \sqrt{3})$ moves parallel to the base line of the prism inside it. Find the angle of incidence for this ray.

A [Delhi I, II, III 2012]

From the diagram, $r = 30^{\circ}$

Also

$n_{21} = \frac{\sin i}{\sin r}$

or,

$\sqrt{3} = \frac{\sin i}{\sin 30^{\circ}}$

or, $\sin i = \sqrt{3} \times \frac{1}{2}$

or, $i = 60^{\circ}$

[CBSE Marking Scheme 2012]

Short Answer Type Questions-II

(3 marks each)

Q. 1. (i) Show using a proper diagram how unpolarized light can be linearly polarised by reflection from a transparent glass surface.

(ii) The figure shows a ray of light falling normally on on the face $A B$ of an equilateral glass prism having refractive index $\frac{3}{2}$ , placed in water of refractive index $\frac{4}{3}$ . Will this ray suffer total internal reflection on striking the face $A C$ ? Justify your answer.

A [CBSE 2018, 2012]

Show Answer

Solution:

Ans. (i) The diagram, showing polarisation by reflection is as shown. [Here the reflected and refracted rays are at right angle to each other.

$\begin{array}{ll} ∴ & r = (\frac{π}{2} - i_{B}) ∴ & μ = (\frac{\sin i_{B}}{\sin r} = \tan i_{B}) \end{array}$

Thus light gets totally polarised by reflection when it is incident at an angle $i_{B}$ (Brewster’s angle), where $i_{B} = \tan^{- 1} μ$

(ii) The angle of incidence, of the ray, on striking the face $AC$ is $i = 60^{\circ}$ (as from figure)

Also, relative refractive index of glass, with respect to the surrounding water, is

For total internal reflection, the required critical angle, in this case, is given by

$\sin i_{C} = \frac{1}{μ} = \frac{8}{9} ≃ 0.89$

$∴ i < i_{C}$

Hence the ray would not suffer total internal reflection on striking the face $A C$ .

[The student may just write the two conditions needed for total internal reflection without analysis of the given case.

The student may be awarded $(1 / 2 + 1 / 2)$ mark in such a case.

[CBSE Marking Scheme 2018]

AT Q. 2. (i) Monochromatic light of wavelength $589 nm$ is incident from air on a water surface. If $μ$ for water is 1.33 , find the wavelength, frequency and speed of the refracted light.

(ii) A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is $20 cm$ .

U [OD I, II, III, 2016]

Ans. (i)

$λ = \frac{589 nm}{1 \cdot 33} = 442 \cdot 8 nm 1 / 2$

Frequency,

$v = \frac{3 \times 10^{8} {ms}^{- 1}}{589 nm}$

$= 5.09 \times 10^{14} Hz$

$1 / 2$

Speed

$v = \frac{3 \times 10^{8}}{1.33} m / s$

(ii)

$\begin{aligned} = 2 \cdot 25 \times 10^{8} m / s & \frac{1}{f} = [\frac{μ_{2}}{μ_{1}} - 1] [\frac{1}{R_{1}} - \frac{1}{R_{2}}] & \frac{1}{20} = [\frac{1.55}{1} - 1] \frac{2}{R} & R = (20 \times 1 \cdot 10) cm = - 22 cm & 1 / 2 \end{aligned}$

$∴ \frac{1}{20} = [\frac{1.55}{1} - 1] \frac{2}{R}$

$∴ R = (20 \times 1 \cdot 10) cm = - 22 cm$

[CBSE Marking Scheme 2016]

किरण प्रकाशिकी और ऑप्टिकल उपकरण

Short Answer Type Questions-II

विषयसूची

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

किरण प्रकाशिकी और ऑप्टिकल उपकरण

Short Answer Type Questions-II

विषयसूची

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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