Question

In Newton's experiment the radii of the $m^{th}$ and $(m+4{)}^{th}$ dark rings are respectively $\sqrt{5}$mm and $\sqrt{7}$mm. What is the value of m?

• A. $2$
• B. $4$
• C. $8$
• D. $10$

Answer 1

The correct option is D $10$

Radius of mth dark fringe $r_m=\sqrt{mR\lambda }$
Thus we get $r_{m+4}=\sqrt{7}=\sqrt{(m+4)R\lambda }$ ......(1)
Also, $r_m=\sqrt{5}=\sqrt{mR\lambda }$ .......(2)
Dividing equation (1) with equation (2),
$\sqrt{\frac{m+4}{m}}=\sqrt{\frac{7}{5}}$
$\frac{m+4}{m}=\frac{7}{5}$
$5(m+4)=7m$
$5m+20=7m$
$2m=20$
$⟹m=10$