The image of an object placed in air formed by a convex refracting surface is at a distance of 10 m behind the surface. The image is real and is at 2^rd3 of the distance of the object from the surface. The wavelength of light inside the surface is 2/3 times the wavelength in air. The radius of the curved surface is x/13 m, the value of x is ______ .

Correct answer: 30. λ_m=λ_aμ⇒μ=3/2 (μ)/v-1/u=(μ-1)/R ⇒3/(2×10)+1/15=(32-1)/R ⇒R=30/13 m =30

Q88 / 90 · JEE Main 2021 (17 Mar Shift 2) · Physics

The image of an object placed in air formed by a convex refracting surface is at a distance of $10 m$ behind the surface. The image is real and is at $\frac{2^{r d}}{3}$ of the distance of the object from the surface. The wavelength of light inside the surface is $\frac{2}{3}$ times the wavelength in air. The radius of the curved surface is $\frac{x}{13} m$ , the value of $x$ is ______ .

Correct answer: 30

$λ_{m} = \frac{λ_{a}}{μ} \Rightarrow μ = \frac{3}{2}$

$\frac{μ}{v} - \frac{1}{u} = \frac{μ - 1}{R}$

$\Rightarrow \frac{3}{2 \times 10} + \frac{1}{15} = \frac{\frac{3}{2} - 1}{R}$

$\Rightarrow R = \frac{30}{13} m$

$= 30$

Hence, the correct answer is 30.