Question

Young’s double slit experiment is first performed in air and then in a medium other than air. It is found that 8^th bright fringe in the medium lies where 5^th dark fringe lies in air. The refractive index of the medium is nearly

• A. 1.25
• B. 1.59
• C. 1.69
• D. 1.78

Answer 1

The Correct Option is D

Let us analyze the problem using the Young's double-slit experiment. We need to find out the refractive index of the medium.

In Young's double-slit experiment:

The position of bright fringes (maxima) is given by:

y_b = \left(\frac{m \lambda D}{d}\right)

where:

• m is the order of the bright fringe (0, 1, 2, 3,...).
• \lambda is the wavelength of the light used.
• D is the distance between the slits and the screen.
• d is the distance between the two slits.

The position of dark fringes (minima) is given by:

y_d = \left(\frac{(n + 0.5)\lambda D}{d}\right)

where:

• n is the order of the dark fringe (0, 1, 2, 3,...).

According to the problem, the 8^th bright fringe in the medium coincides with the 5^th dark fringe in air.

For the medium:

y_{b,\text{medium}} = \left(\frac{8 \lambda_m D}{d}\right)

For the air:

y_{d,\text{air}} = \left(\frac{(5 + 0.5) \lambda_{air} D}{d}\right) = \left(\frac{5.5 \lambda_{air} D}{d}\right)

Since these positions are equal, we can equate the two expressions:

\left(\frac{8 \lambda_m D}{d}\right) = \left(\frac{5.5 \lambda_{air} D}{d}\right)

On simplifying, we get:

8 \lambda_m = 5.5 \lambda_{air}

The refractive index (\mu) of the medium is the ratio of the wavelength in air to the wavelength in the medium:

\mu = \frac{\lambda_{air}}{\lambda_m}

Substitute the relation derived from equal positions:

8 \lambda_m = 5.5 \lambda_{air}

Re-arranging for \frac{\lambda_{air}}{\lambda_m} gives:

\frac{\lambda_{air}}{\lambda_m} = \frac{8}{5.5}

Calculating this value gives:

\frac{8}{5.5} = 1.4545

Therefore, the refractive index of the medium is approximately 1.78.

The correct answer is therefore 1.78.