Question
Obtain the angular magnification for the image formed at infinity for simple microscope.
✓
Answer
→When an object of height $h$ is placed at the near point as shown in the figure (a), the angle subtended at the eye by the object is $\theta_0$.
→from figure, $\tan \theta_0=\frac{h}{ D }$
for small angle, $\tan \theta_0 \approx \theta_0=\frac{h}{ D }......(1)$
→As shown in figure (b), if an object of height $h$ is placed at the principal focus, its image will be at an infinite distance. This time, the angle subtended at the eye by the object is $\theta_i$.
→from figure, $\tan \theta_i=\frac{h}{f}$
but for small angle, $\tan \theta_i \approx \theta_i=\frac{h}{f}......(2)$
→angular magnification of lens,
$\begin{aligned}m & =\frac{\theta_i}{\theta_0}=\frac{\frac{h}{f}}{\frac{h}{ D }}=\frac{h}{f} \times \frac{ D }{h} \\\therefore m & =\frac{ D }{f}\end{aligned}$
→This is the magnification when the image is at infinity.
→Thus, the magnification obtained with simple microscope is between $\frac{ D }{f}$ to $1+\frac{ D }{f}$.
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