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:
- 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.
