A thin lens focal length f1 and its aperture has diameter d. It forms an image of intensity I. Now the central part of the aperture up to diameter (d/2) is blocked by an opaque paper. The focal length and image intensity will change to

Question

A thin lens focal length f1 and its aperture has diameter d. It forms an image of intensity I. Now the central part of the aperture up to diameter (d/2) is blocked by an opaque paper. The focal length and image intensity will change to (A) (f/2) and (I/2) (B) f and (I/4) (C) (3 f/4) and (I/2) (D) f and (3 I/4)

Tardigrade Admin · Accepted Answer

I propto A2 ⇒ (I2/I1)=((A2/A1))2 =(π r2-(π r2/4)/π r2)=(3/4) ⇒ I2=(3/4) I1 and focal length remains unchanged.

Q. A thin lens focal length $f_{1}$ and its aperture has diameter $d$ . It forms an image of intensity $I$ . Now the central part of the aperture up to diameter $\frac{d}{2}$ is blocked by an opaque paper. The focal length and image intensity will change to

$\frac{f}{2}$ and $\frac{I}{2}$

$f$ and $\frac{I}{4}$

$\frac{3 f}{4}$ and $\frac{I}{2}$

$f$ and $\frac{3 I}{4}$

$I \propto A^{2} \Rightarrow \frac{I _{2}}{I _{1}} = (\frac{A _{2}}{A _{1}})^{2}$
$= \frac{π r ^{2} - \frac{π r ^{2}}{4}}{π r ^{2}} = \frac{3}{4}$
$\Rightarrow I_{2} = \frac{3}{4} I_{1}$ and focal length remains unchanged.

Q. A thin lens focal length f1​ and its aperture has diameter d. It forms an image of intensity I. Now the central part of the aperture up to diameter 2d​ is blocked by an opaque paper. The focal length and image intensity will change to

2f​ and 2I​

f and 4I​

43f​ and 2I​

f and 43I​