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  4. Newton's rings are observed. normally in reflected light of wavelength 5000 mathring A . The diameter of the 10th dark ring is 0.005 m. The radius of curvature of the lens is

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Q. Newton's rings are observed. normally in reflected light of wavelength $5000 \mathring A$ . The diameter of the 10$^{th}$ dark ring is 0.005 m. The radius of curvature of the lens is

COMEDKCOMEDK 2014Wave Optics

Solution:

Diameter of $n^{th}$ dark ring,
$D_n = 2 \sqrt{n \lambda R}$
$ \therefore \, \, R = \frac{D^2_n}{4n \lambda}$
Here, $n = 10, D_{10} = 0.005 \: m$
$ \lambda = 5000 \mathring A = 5000 \times 10^{-10} m = 5\times 10^{-7} m$
$\therefore R= \frac{\left(0.005 m\right)^{2}}{4\times 10\times 5\times 10^{-7}m} = 1.25 m $