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 $600 nm$ is used. If the wavelength of light is changed to $400 nm$, number of fringes observed in the same segment of the screen is given by

(2001, 2M)

(a) 12

(b) 18

(c) 24

(d) 30

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Solution:

  1. Fringe width, $\omega=\frac{\lambda D}{d} \propto \lambda$

When the wavelength is decreased from $600 nm$ to $400 nm$, 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 $\omega \propto \lambda$, therefore, if YDSE apparatus is immersed in a liquid of refractive index $\mu$, the wavelength $\lambda$ and thus the fringe width will decrease $\mu$ times.



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