Calculate wavelength of light used when limit of resolution of the microscope is `5 xx 10^(-7) m` and cone angle of light falling on the objective is equal to `90^(@)`. Given for air, `mu = 1`.

Answer

`0.707 xx 10^(-6)m`

Explanation

Here, `lambda = ?`
Limit of resolution, `d = 5 xx 10^(-7)m`
`2 theta = 90^(@)` or `theta = 45^(@), mu = 1`
As `d = (lambda)/(2mu sin theta)`
`:. lambda = 2 mu d sin theta = 2 xx 1 xx 5 xx 10^(-7) sin 45^(@)`
`lambda = 10^(-6) xx (1)/(sqrt(2)) = 0.707 xx 10^(-6)m`