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

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

1.59

1.78

1.25

1.69

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

In Young's double slit experiment, the position of bright and dark fringes depends on the wavelength of light and the medium through which it travels. When light passes through a medium other than air, its speed changes due to the change in the refractive index, which also affects the fringe positions.

In air, the fringe positions are determined by the wavelength of light in air ( $\lambda_{\text{air}}$ $λ$ $air$ $$ ), and the formula for the position of the $m$ $m$ -th bright fringe is:

${y_1} = {y_2} \Rightarrow \frac{{(\Delta {x_1})D}}{d} = \frac{{(\Delta {x_2})D}}{d}\$

$\Rightarrow {\eta _1}{\lambda _m} = \frac{{(2{n_2} - 1){\lambda _a}}}{2}\$ $;\,8{\lambda _m} = \frac{{(2 \times 5 - 1){\lambda _a}}}{2}\,;\$

$\frac{8}{{4.5}} = \frac{{{\lambda _a}}}{{{\lambda _m}}} = \mu \,\,;$ $\mu = \frac{{16}}{9} = 1.77\$

By using the relationship between the positions of the fringes, we can derive the refractive index $n$ $n$ . Since the positions of the fringes are directly proportional to the wavelength, we can conclude that the refractive index of the medium is $n = 1.78$ n=1.78, which is the correct answer. This means the light slows down in the medium, reducing the fringe separation compared to air

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE