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प्रश्न
An optical instrument used for angular magnification has a 25 D objective and 20 D eyepiece. The tube length is 25 cm when the eye is least strained. (a) Whether it is a microscope or a telescope? (b) What is the angular magnification produced?
उत्तर
Given:
Power of the objective lens = 25 D
The focal length of the objective lens is given by
`f_0 =1/(25D)` = 0.04 cm
Power of the eyepiece = 5 D
The focal length of the eyepiece is given by
`f_e =1/(20D)` =0.05 m = 5 cm
(a) As f0 < fe , he instrument must be a microscope.
(b) Tube length,l = 25 cm
Image distance for the eye lens, ve = 25 cm
We know :
l = vo +fe
⇒ v0 = l - fe =25 -5 = 20 cm
On applying the lens formula for the objective lens , we get :
`1/v_0 -1/u_0 = 1/f_0`
`=> -1/u_0 =1/4 - 1/20`
`=> -1/u_0 = (5-1)/20 =4/20`
`=> u_0 = 20/4 = 5 text/"cm"`
The angular magnification of microscope (m) is given by
`m = v_0/u_0 (D/f_e)`
= `20/5 (25/5)` = 20 cm
So, the required angular magnification of the microscope is 20.
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