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STD 12 - 9. Ray optics abd optical instruments — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 9. Ray optics abd optical instruments4 Marks
MCQ
Figures shows a convex lens cut symmetrically into two equal halves and separated laterally by a distance $h.$ A point object placed at a distance $30\, cm,$ from the lens halves, forms two real images separated by a distance $d$. A plot of $d$ versus $h$ is shown in figure. The focal length of the lens is ......$cm$
  • A
    $60$
  • B
    $40$
  • C
    $45$
  • ✓
    $20$
✓

Answer

Correct option: D.
$20$
d
Image distance from each part of the lens $=v=\frac{u f}{u+f}$

$\Longrightarrow M=\frac{v}{u}=\frac{f}{u+f}=\frac{f}{f-30}$

Thus the distance of each image from corresponding principle axis $=M \frac{h}{2}$

Thus distance of image from dotted line $=\frac{h}{20}+M \frac{h}{2}=(M+1) \frac{h}{2}$

Thus the distance between the objects $=d=(M+1) h=\frac{2 f-30}{f-30} h$

$\Longrightarrow \frac{d}{h}=\frac{2 f-30}{f-30}=3$

$\Longrightarrow f=60 \mathrm{cm}$

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