The ratio of the focal lengths of a convex le | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The lens maker's formula is given by $\frac{1}{f} = (\mu_g - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$.For a lens in air $(\mu_a = 1)$: $\f

Vedclass · Accepted Answer

$1.20$

Vedclass · Answer

(A) The lens maker's formula is given by $\frac{1}{f} = (\mu_g - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} ight)$.For a lens in air $(\mu_a = 1)$: $\frac{1}{f_a} = (\mu_l - 1) K$,where $K = (\frac{1}{R_1} - \frac{1}{R_2})$.For a lens in liquid $(\mu_{liq})$: $\frac{1}{f_l} = (\frac{\mu_l}{\mu_{liq}} - 1) K$.Given $\frac{f_a}{f_l} = \frac{1}{2}$,we have $\frac{f_l}{f_a} = 2$.Dividing the two equations: $\frac{f_a}{f_l} = \frac{(\frac{\mu_l}{\mu_{liq}} - 1)}{(\mu_l - 1)} = \frac{1}{2}$.Substituting $\mu_l = 1.5$: $\frac{(\frac{1.5}{\mu_{liq}} - 1)}{(1.5 - 1)} = \frac{1}{2}$.$\frac{1.5}{\mu_{liq}} - 1 = 0.5 	imes 0.5 = 0.25$.$\frac{1.5}{\mu_{liq}} = 1.25$.$\mu_{liq} = \frac{1.5}{1.25} = 1.2$.

The ratio of the focal lengths of a convex lens when kept in air and when it is immersed in a liquid is $1: 2$. If the refractive index of the material of the lens is $1.5$,then the refractive index of the liquid is

Similar Questions

The sun subtends an angle of $0.5^{\circ}$ at the earth's surface. Its image is formed by a convex lens of focal length $50 \ \text{cm}$. The diameter of the image will be (in $\text{mm}$)

Two convex lenses of focal lengths $f_1$ and $f_2$ form images with magnification $m_1$ and $m_2$, when used individually for an object kept at the same distance from the lenses. Then, $f_1 / f_2$ is

The distance between an object and the screen is $100 \ cm$. $A$ lens produces an image on the screen when placed at either of the positions $40 \ cm$ apart. The power of the lens is

$A$ lens behaves as a converging lens in air but a diverging lens in water,then the refractive index $(\mu)$ of its material is

The focal lengths for violet,green,and red light rays are ${f_V}$,${f_G}$,and ${f_R}$ respectively. Which of the following is the true relationship?

Vedclass Test Series

Exam Paper Generator

Online Exam Module