Question

A small object A is placed on the principal axis of an equiconvex lens at a distance of $30cm$. The refractive index of the glass of the lens is 1.5 and its surfaces have radius of curvature, $R=20cm$. Two glass slabs $S_1$ and $S_2$ have been placed behind the lens as shown. Thickness of the two slabs are $6cm$ and $4cm$ respectively & refractive indices are $\frac{3}{2}$ and 2 respectively.

• A. The distance of final image measured from lens is 60 $cm$ and the magnification is -2
• B. The distance of final image measured from lens is 40 $cm$ and the magnification is -3.
• C. If slab $S_2$ is moved to the left so as to put into contact with $S_1$ image shifts to left by 2 $cm$.
• D. If slab $S_2$ is moved to the left so as to put into contact with $S_1$ into contact with $S_1$ , image does not shift.

Answer 1

Answer: (A), (D)

The correct options are
A The distance of final image measured from lens is 60 $cm$ and the magnification is -2
D If slab $S_2$ is moved to the left so as to put into contact with $S_1$ into contact with $S_1$ , image does not shift.

For lens,
$\frac{1}{f}=(\mu -1)\left[\frac{2}{R}\right]=(1.5-1)\left[\frac{2}{R}\right]\Rightarrow f=R=20cm$
$\text{Using lens equation,}\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\Rightarrow \frac{1}{v}-\left(\frac{1}{-30}\right)=\frac{1}{20}$
$\Rightarrow v=60cm$
Shift due to $S_1$ is , $t_1[1-\frac{1}{{\mu }_1}]=6[1-\frac{2}{3}]=2cm$
Shift due to $S_2$ is , $t_2[1-\frac{1}{{\mu }_2}]=4[1-\frac{1}{2}]=2cm$
$\therefore$ Final image will be at a distance of 60 +2+2 = 64 $cm$ from lens.
Position of image will not change if slab is moved.
Magnification, $m=\frac{v}{u}$ [for lens]
$\Rightarrow m=\frac{60}{-30}=-2$