ln Young's double-slit experiment, the fringe width with the light of wavelength), λ = 600 nm is 3 mm. The fringe width, when the λ, of light, is changed to 400 nm is

Concept:

• YDSE (Young’s Double Slit Experiment): If a monochromatic light falls on two narrow slits which are very close to each other and act as coherent sources superposing each other and an interference pattern is observed on the screen.

The fringe width is given by:

\(\beta = \frac{{\lambda D}}{d}\)

Where λ is the wavelength of light used, D = distance of the screen from the slits, d = distance between two slits.

EXPLANATION:

Fringe width, \(\beta = \frac{{\lambda D}}{d}\)

Calculation:

Given,

When wavelength (λ) = 600 nm = 600 × 10^-9 m

Fringe width (β) = 3 mm = 3 × 10^-3 m

We know that,

\(\beta = \frac{{\lambda D}}{d}\; \Rightarrow \frac{\beta }{\lambda } = \frac{D}{d} = \frac{{3 \times {{10}^{ - 3}}\;m}}{{600 \times {{10}^{ - 9}}\;m}} = 5 \times {10^3}\)

Now,

λ = 400 nm = 400 × 10^-9 m

\( \Rightarrow \beta = \frac{{\lambda D}}{d} = \lambda \;\left( {\frac{D}{d}} \right) = 400 \times {10^{ - 9}}\;m \times \left( {5 \times {{10}^3}} \right) = 2 \times {10^{ - 3}}\;m = 2\;mm\)

Now, the width is 2 mm