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Ray Optics and Optical Instruments — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsRay Optics and Optical Instruments5 Marks
Question
An optical instrument used for angular magnification has a $25D$ objective and a $20D$ eyepiece. The tube length is $25\ cm$ when the eye is least strained.
  1. Whether it is a microscope or a telescope?
  2. What is the angular magnification produced?
✓

Answer

The optical instrument has $\text{f}_0=\frac{1}{25\text{D}}=0.04\text{m}=4\text{cm}$
$\text{f}_\text{e}=\frac{1}{20\text{D}}=0.05\text{m}=5\text{cm}$
tube length $= 25\ cm\ ($normal adjustment$)$
  1. The instrument must be a microscope as $f_0< f_e$
  2. Since the final image is formed at infinity, the image produced by the objective should lie on the focal plane of the eye piece.
So, image distance for objective $= v_0 = 25 – 5 = 20\ cm$
Now, using lens formula.
$\frac{1}{\text{v}_0}-\frac{1}{\text{u}_0}=\frac{1}{\text{f}_0}$
$\Rightarrow\frac{1}{\text{u}_0}=\frac{1}{\text{v}_0}-\frac{1}{\text{f}_0}=\frac{1}{20}-\frac{1}{4}$
$=\frac{-4}{20}=\frac{-1}{5}$
$\Rightarrow\text{u}_0=-5\text{cm}$
So, angular magnification $\text{m}=-\frac{\text{v}_0}{\text{u}_0}\times\frac{\text{D}}{\text{f}_\text{e}}\ [$Taking $D = 25\ cm]$
$=-\frac{20}{-5}\times\frac{25}{5}=20$

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