A biconvex lens is cut into two halves along | vedclass

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

Question

(A) For a biconvex lens with refractive index $\mu$ and radii of curvature $R_1 = R$ and $R_2 = -R$, the lens maker's formula is: $\frac{1}{f} = (\mu

Vedclass · Accepted Answer

$f' = 2f, f'' = f$

Vedclass · Answer

(A) For a biconvex lens with refractive index $\mu$ and radii of curvature $R_1 = R$ and $R_2 = -R$, the lens maker's formula is: $\frac{1}{f} = (\mu - 1)(\frac{1}{R} - \frac{1}{-R}) = (\mu - 1)(\frac{2}{R})$.Case $(i)$: When the lens is cut along the principal axis $(XOX')$, each half is a plano-convex lens with radii of curvature $R$ and $\infty$. The focal length $f'$ is given by $\frac{1}{f'} = (\mu - 1)(\frac{1}{R} - \frac{1}{\infty}) = \frac{\mu - 1}{R}$. Comparing this with the original formula, we get $f' = 2f$.Case $(ii)$: When the lens is cut perpendicular to the principal axis $(YOY')$, each half remains a biconvex lens with radii of curvature $R$ and $-R$, but the aperture is halved. The focal length $f''$ is given by $\frac{1}{f''} = (\mu - 1)(\frac{1}{R} - \frac{1}{-R}) = (\mu - 1)(\frac{2}{R})$. Thus, $f'' = f$.Therefore, the correct option is $(A)$.

$A$ biconvex lens is cut into two halves along $(i) XOX'$ and $(ii) YOY'$ as shown in the figure. Let $f, f', f''$ be the focal lengths of the complete lens, of each half in case $(i),$ and of each half in case $(ii),$ respectively. Choose the correct statement from the following:

Similar Questions

The image distance of an object placed $10 \ cm$ in front of a thin lens of focal length $+ 5 \ cm$ is......$cm$.

An object of height $1.5 \ cm$ is placed on the axis of a convex lens of focal length $25 \ cm$. $A$ real image is formed at a distance of $75 \ cm$ from the lens. The size of the image will be........$cm$.

The two surfaces of a concave lens, made of glass of refractive index $1.5$, have the same radii of curvature $R$. It is now immersed in a medium of refractive index $1.75$. Then the lens:

$A$ convex lens of focal length $f$ produces a real image $n$ times the size of the object. The image distance is

Vedclass Test Series

Exam Paper Generator

Online Exam Module