Name: Total Internal Reflection From Prism
Uploaded: 2019-07-19
Duration: 1 min 56 s
Description: You must have seen reflectors on a bicycle. Why are they attached to the mudguards? What use do they have? Let’s watch this video on reflectors to find out.

Question

Describe the terrestrial telescope under the following points: Derivation of formula for magnifying power when the image is formed at least distance of distinct vision.

Accepted Answer

When the final image is formed at the least distance of distinct vision:
The object is situated far away, so the image formed on the objective is equal to the visual angle formed on the eyepiece.

Because these $α$ and $β$ angles are very small.

Thus, $\tan α \approx α$ and $\tan β \approx β$
$∴ m = \frac{β}{α} = \frac{\tan β}{\tan α}$ ⋯⋯⋯(1)
From the above figure, we have:

$\tan α = \frac{P Q}{O Q} = \frac{P' Q'}{O Q'}$

$\tan β = \frac{P' Q'}{Q' O}$

Putting values of $\tan α$ and $\tan β$ in equation(1), we get:

$m = \frac{\frac{P' Q'}{Q' O}}{\frac{P' Q'}{O Q'}}$

or $m = \frac{P' Q' \times O' Q}{Q' O \times P' Q'} = \frac{O' Q}{O Q'}$

But, $O' Q = f_{0}$ and $O Q' = - u_{e}$

$∴ m = - \frac{f_{0}}{u_{e}}$ [by sign convention]
When image is formed at the least distance of distinct vision,

Using the lens formula,
$u_{e} = \frac{f_{e}}{1 + \frac{f_{e}}{D}}$

$∴ m = \frac{f_{0}}{f_{e}} (1 + \frac{f_{e}}{D})$
The above equation gives a formula for magnifying power when the final image is formed at the least distance of distinct vision.

Describe the terrestrial telescope under the following points: Derivation of formula for magnifying power when the image is formed at least distance of distinct vision.

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