Question

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

• A. 12
• B. 18
• C. 24
• D. 30

Answer 1

Answer: (B)

18

Answer 2

Fringe width, $\omega=\frac{\lambda D}{d}∝\lambda$

When the wavelengthis decreased from 600 nm to 400 nm, the 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, the number of fringes observed in the same segment $=12\times\frac{3}{2}=18$

Note: Since $\omega∝\lambda$, therefore, if the YDSE apparatus is immersed in a liquid of refractive index $\mu$, the wavelength $\lambda$ and thus the fringe width will decrease $\mu$ times.