As observed from the top of a 100 m high light house from the sea level, the angles of depression of two ships are `30^@` and `45^@` If one ship is exactly behind the other one on the same side of the light house, find the distance between the two ships.

Explanation

Data: `lambda= 4800 Å= 4.8 xx 10^(7) m, d=2.4 mm = 2.4 xx 10^(-3)`m,
D= Distance between the slit and biprism + distance between the biprism and eyepiece = `-20+ 100 = 120 cm = 1.2m`
The distance of the nth bright band from the central band is
`X_(nb) = nlambdaD/d`
`therefore x(4b) = (4lambdaD)/d = (4 xx 4.8 xx 10^(-7) xx 1.2)/(2.4 xx 10^(-3)) = 9.6 xx 10^(-4)`m
The distance of he nth dark band from the central band is
`x_(md) = (2m-1)(lambda/2)D/d`
`therefore x_(4d) = (2 xx 4 -1)(4.8 xx 10^(-7))/(2) xx 1.2/(2.4 xx 10^(-3)) = 8.4 xx 10^(-4)`m
`therefore x_(4b) + x_(4d) = 9.6 xx 10^(-4) + 8.4 + 10^(-4)`
`=18 xx 10^(-4) = 1.8 xx 10^(-3)m` (or 1.8 mm)
This gives the distance between the 4th bright and the 4th dark bands on the opposite sides of the central band.