A beam of light consisting of two wavelengths | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For the bright fringes of two different wavelengths to coincide at a distance $x$ from the central maximum,the condition is given by: $x = \frac{n

Vedclass · Accepted Answer

$0.156$

Vedclass · Answer

(A) For the bright fringes of two different wavelengths to coincide at a distance $x$ from the central maximum,the condition is given by: $x = \frac{n_1 \lambda_1 D}{d} = \frac{n_2 \lambda_2 D}{d}$ This implies $n_1 \lambda_1 = n_2 \lambda_2$,where $n_1$ and $n_2$ are the orders of the bright fringes. Rearranging the terms,we get: $\frac{n_1}{n_2} = \frac{\lambda_2}{\lambda_1} = \frac{5200 \mathring{A}}{6500 \mathring{A}} = \frac{4}{5}$ For the least distance,we take the smallest integer values: $n_1 = 4$ and $n_2 = 5$. Now,substituting these values into the formula for $x$: $x = \frac{n_1 \lambda_1 D}{d} = \frac{4 	imes 6500 	imes 10^{-10} 	ext{ m} 	imes 1.2 	ext{ m}}{2 	imes 10^{-3} 	ext{ m}}$ $x = \frac{4 	imes 6500 	imes 1.2 	imes 10^{-10}}{2 	imes 10^{-3}} 	ext{ m} = 15600 	imes 10^{-7} 	ext{ m} = 1.56 	imes 10^{-3} 	ext{ m}$ $x = 0.156 	ext{ cm}$.

Similar Questions

$A$ Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

In Young's double slit experiment,$62$ fringes are seen in the visible region for sodium light of wavelength $5893 \ \mathring{A}$. If violet light of wavelength $4358 \ \mathring{A}$ is used in place of sodium light,then the number of fringes seen will be:

Two slits at a distance of $1\, mm$ are illuminated by light of wavelength $6.5 \times 10^{-7}\, m$. The interference fringes are observed on a screen placed at a distance of $1\, m$. The distance between the third dark fringe and the fifth bright fringe will be......$mm$.

In an interference pattern,if the ratio of slit widths is $1:9$,find the ratio of maximum to minimum intensity.

Vedclass Test Series

Exam Paper Generator

Online Exam Module