SATHEE: Optics 6 Question 22

Optics 6 Question 22

24. In a Young’s double slit experiment, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength $600 n m$ is used. If the wavelength of light is changed to $400 n m$ , number of fringes observed in the same segment of the screen is given by

(2001, 2M)

(a) 12

(b) 18

(d) 30

Show Answer

Solution:

Fringe width, $ω = \frac{λ D}{d} \propto λ$

When the wavelength is decreased from $600 n m$ to $400 n m$ , fringe width will also decrease by a factor of $\frac{4}{6}$ or $\frac{2}{3}$ or the number of fringes in the same segment will increase by a factor of $3 / 2$ .

Therefore, number of fringes observed in the same segment

$= 12 \times \frac{3}{2} = 18$

NOTE Since $ω \propto λ$ , therefore, if YDSE apparatus is immersed in a liquid of refractive index $μ$ , the wavelength $λ$ and thus the fringe width will decrease $μ$ times.

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Optics 6 Question 22

24. In a Young’s double slit experiment, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength 600nm is used. If the wavelength of light is changed to 400nm, number of fringes observed in the same segment of the screen is given by

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24. In a Young’s double slit experiment, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength $600 n m$ is used. If the wavelength of light is changed to $400 n m$ , number of fringes observed in the same segment of the screen is given by