SATHEE: wave-optics Question 24

wave-optics Question 24

Question: Q. 9. Answer the following questions :

(i) In a double slit experiment using light of wavelength $600 nm$ , the angular width of the fringe formed on a distant screen is ${0.1}^{\circ}$ . Find the spacing between the two slits.

(ii) Light of wavelength $5000 \AA$ propagating in air gets partly reflected from the surface of water. How will the wavelengths and frequencies of the reflected and refracted light be affected?

A [Delhi I, II, III 2015]

Show Answer

Solution:

Ans. Finding the spacing between two slits 1 Effect on wavelength and frequency of reflected and refracted width light.

(i) Angular width of fringes :

$θ = \frac{λ}{d}$

where, $d =$ separation between two slits

Here $θ = 0 \cdot 1^{\circ} = 0 \cdot 1 \times \frac{π}{180}$ radian

$\begin{aligned} ∴ d & = \frac{600 \times 10^{- 9} \times 180}{0.1 \times π} m & = 3.43 \times 10^{- 4} m & = 0.34 mm \end{aligned}$

(ii) For Reflected light :

Wavelength remains same

Frequency remains same

For Refracted light :

Wavelength decreases

Frequency remains same

[CBSE Marking Scheme 2015]

Detailed Answer :

(b) Incident ray Reflected ray

we know that frequency of light is same in all media Thus,

$\begin{aligned} f & = \frac{v}{λ} = \frac{3.0 \times 10^{8}}{5000 \times 10^{- 10}} & = 0.6 \times 10^{+ 15} & = 0.6 \times 10^{15} Hz \end{aligned}$

If wavelength in air is $Misplaced &$ that in water is $λ_{2}$ .

$\begin{aligned} μ_{2} = \frac{v_{2}}{v_{1}} = \frac{λ_{2}}{λ_{1}} & λ_{2} = λ_{1} (\frac{μ_{1}}{μ_{2}}) & λ_{2} = 5000 (\frac{μ_{1}}{μ_{2}}) \AA \end{aligned}$

Wavelength of refracted ray decreases by a factor of $(\frac{μ_{1}}{μ_{2}})$ while wavelength of reflected ray may remains same.

Wave Optics

wave-optics Question 24

A [Delhi I, II, III 2015]

Detailed Answer :

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Wave Optics

wave-optics Question 24

A [Delhi I, II, III 2015]

Detailed Answer :

Long Answer Type Questions

Table of Contents

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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