Question

The 630 nm light from a helium neon laser irradiates a grating. The light then falls on a screen where the first bright spot is separated from the central maxim by 0.51m. Light of another wavelength produces its first bright spot at 0.39 m from its central maximum. Determine the second wavelength.

Answer 1

Answer:

The second wavelength is 482 nm.

Explanation:

Given that,

Wavelength = 630 nm

Distance from central maxim = 0.51 m

Distance from central maxim of another wavelength = 0.39 m

We need to calculate the second wavelength

Using formula of width of fringe

$\beta=\dfrac{\lambda d}{D}$

Here, d and D will be same for both wavelengths

$\lambda$ = wavelength

$\beta$ = width of fringe

The width of fringe for first wavelength

$\beta_{1}=\dfrac{\lambda_{1} d}{D}$....(I)

The width of fringe for second wavelength

$\beta_{2}=\dfrac{\lambda_{2} d}{D}$....(II)

Divided equation (I) by equation (II)

$\dfrac{\beta_{1}}{\beta_{2}}=\dfrac{\lambda_{1}}{\lambda_{2}}$

$\lambda_{2}=\dfrac{630\times10^{-9}\times0.39}{0.51}$

$\lambda_{2}=4.82\times10^{-7}$

$\lambda=482\ nm$

Hence, The second wavelength is 482 nm.