The fringe width at a distance of 50cm from the slits in Young's experiment for light of wavelength 6000Angstrom is 0.048cm. Find the fringe width at the same distance for wavelength=5000aAngstrom?

Answer 1

We can use the formula for fringe width in Young's double slit experiment:

β = λD/d

where β is the fringe width, λ is the wavelength of light, D is the distance from the slits to the screen, and d is the distance between the two slits.

Given:
λ1 = 6000 Å
λ2 = 5000 Å
D = 50 cm
β1 = 0.048 cm

Using the formula for β1, we can find d1:

d1 = λ1D/β1 = (6000 Å) (50 cm) / (0.048 cm) = 6.25 x 10^6 Å = 0.625 mm

Now we can use d1 to find β2:

β2 = λ2D/d1 = (5000 Å) (50 cm) / (0.625 mm) = 0.4 cm

Therefore, the fringe width at a distance of 50 cm from the slits for light of wavelength 5000 Å is 0.4 cm.