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Optical Instruments — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsOptical Instruments5 Marks
Question
An optical instrument used for angular magnification has a 25D objective and a 20D eyepiece. The tube length is 25cm 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 = 25cm (normal adjustment)

  1. The instrument must be a microscope as f0 < fe
  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 = v0 = 25 – 5 = 20cm

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 = 25cm]

$=-\frac{20}{-5}\times\frac{25}{5}=20$

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