A double convex lens has power P and same rad | vedclass

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

Question

(D) For a double convex lens, the radii of curvature are $R_1 = R$ and $R_2 = -R$. Using the lens maker's formula, the power $P$ is given by:$P = (\mu

Vedclass · Accepted Answer

$0.33$

Vedclass · Answer

(D) For a double convex lens, the radii of curvature are $R_1 = R$ and $R_2 = -R$. Using the lens maker's formula, the power $P$ is given by:$P = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) = (\mu - 1) \left( \frac{1}{R} - \frac{1}{-R} \right) = (\mu - 1) \left( \frac{2}{R} \right) \quad ...(i)$For a plano-convex lens, the radii of curvature are $R_1' = R'$ and $R_2' = \infty$. The power $P'$ is given by:$P' = (\mu - 1) \left( \frac{1}{R'} - \frac{1}{\infty} \right) = (\mu - 1) \left( \frac{1}{R'} \right) \quad ...(ii)$Given that $P' = 1.5P = \frac{3}{2}P$, we substitute the expressions from $(i)$ and $(ii)$:$(\mu - 1) \left( \frac{1}{R'} \right) = \frac{3}{2} \left[ (\mu - 1) \left( \frac{2}{R} \right) \right]$$\frac{1}{R'} = \frac{3}{R}$Therefore, $R' = \frac{R}{3} \approx 0.33R$.

$A$ double convex lens has power $P$ and same radii of curvature $R$ of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power $1.5P$ is ......$R$.

Similar Questions

Focal length of a convex lens is $20 \ cm$ and its refractive index is $1.5$. It produces an erect,enlarged image if the distance of the object from the lens is: (in $cm$)

$A$ glass concave lens is placed in a liquid in which it behaves like a convergent lens. If the refractive indices of glass and liquid with respect to air are $^a{\mu _g}$ and $^a{\mu _l}$ respectively,then

$A$ thin glass (refractive index $1.5$) lens has an optical power of $-5 D$ in air. Its optical power in a liquid medium with a refractive index of $1.6$ will be:

$A$ magnifying lens has a focal length of $10 \, cm$. If an image is to be formed at a distance of $30 \, cm$ from the lens,the object should be placed at a distance of ..... $cm$.

The distance $v$ of the real image formed by a convex lens is measured for various object distances $u$. $A$ graph is plotted between $v$ and $u$. Which one of the following graphs is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module