Question

Laser light of wavelength 630 nm incident on a pair of slits produces an interference pattern in which the bright fringes are separated by 8.1 mm. A second light produces an interference pattern in which the fringes are separated by 7.2 nun. Calculate the wavelength of the second light.

Answer 1

Answer: The wave length of the second light is 560 nm.

Explanation:

Given that,

Wavelength of first light $\lambda = 630\ nm$

Separation between bright fringes $y = 8.1 mm$

Fringe separation of second light $y= 7.2\ mm$

We know ,

$y = \dfrac{mD\lambda}{d}$

Where, y = fringe separation

d = slit width

D = distance of screen from slit

m = order of fringe

Now, for first light

$8.1\ mm = \dfrac{mD\times630\ nm}{d}$...(I)

For second light

$7.2\ mm = \dfrac{mD\times \lambda}{d}$....(II)

Now, equation(II) divided by equation(I)

Therefore,

$\dfrac{\lambda}{630\ nm}= \dfrac{7.2\ mm}{8.1\ mm}$

$\lambda = 560\ nm$

Hence, the wave length of the second light is 560 nm.