Question

Two sources of light that both have

wavelengths equal to 700nm are separated

by a horizontal distance x. They are 5.00 m

from a vertical slit of width 0.500 mm. What

is the smallest value of x for which the

diffraction pattern of the sources can be

resolved by Rayleigh’s criterion ​

Answer 1

Given:

Two sources of light that both have  wavelengths equal to 700nm are separated  by a horizontal distance x. They are 5.00 m  from a vertical slit of width 0.500 mm.

To find:

What  is the smallest value of x for which the  diffraction pattern of the sources can be  resolved by Rayleigh’s criterion .

Solution:

From given, we have,

Two sources of light that both have  wavelengths equal to 700nm are separated  by a horizontal distance x.

They are 5.00 m  from a vertical slit of width 0.500 mm.

⇒ λ = 700 nm

⇒ L = 5.00 m

⇒ a = 0.500 mm

here, we use the formula,

x = λL/a

x = (700 nm × 5 m) / 0.500 mm = 7.00 mm

∴ x = 7.00 mm

Therefore, the smallest value of x for which the  diffraction pattern of the sources can be  resolved by Rayleigh’s criterion is 7 mm.