Q144 / 180 · COMEDK 2014 · Physics

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

  • A
    $1 \mathrm{~m}$
  • Correct answer
    B
    $1.25 \mathrm{~m}$
  • C
    $2 \mathrm{~m}$
  • D
    $0.5 \mathrm{~m}$

Solution

In Newton's ring experiment, diameter of $n$th dark ring, $D_{n}=2 \sqrt{n \lambda R}$ $\Rightarrow$ $R=\frac{D_{n}^{2}}{4 n \lambda}$ ...(i) Given, $n=10, D_{10}=0.005 \mathrm{~m}$ $\lambda=5000 Å=5 \times 10^{-7} \mathrm{~m}$ $\therefore$ Putting these values in Eq. (i), we get $$ R=\frac{(0.005)^{2}}{4 \times 10 \times 5 \times 10^{-7}}=1.25 \mathrm{~m} $$

Hence, the correct answer is option: 'B'.

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