Calculate the wavelength of light used in an interference experiment from the following data: Fringe width = 0.03 cm. Distance between slits and eyepiece through which the interference pattern is observed is 1 m. Distance between the images of the virtural when a convex lens of focal length 16 cm is used at a distance of 80 cm from the eyepiece is 0.8 cm.

Options

A. `6000 Å`
B. `0.00006 Å`
C. 6000 cm
D. 0.00006 m

Answer

a

Explanation

`beta = 0.3 cm. D = 1 m = 100 cm`
Distance between images of the sources `0.8 cm`
Distance of images from lens, `v = 80 cm`
Distance of slit from lens`=u`
`(1)/(v) + (1)/(u) = (1)/(f) implies (1)/(60) + (1)/(u) = (1)/(16) implies u = 20 cm`
Magnification `= (v)/(u) = (80)/(20) = 4`
Magnification `= ("Distance between images of slits")/("Distance between slits")`
`= (0.8)/(d) = (0.8)/(d) = 4`
` implies d = 0.2 m implies beta = (D lambda)/(d) = (100 lambda)/(2) = 0.03`
`implies lambda = 6000 Å`.