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Chapter 35: Q. 35 (page 1018)

The objective lens of a telescope is a symmetric glass lens with $100 c m$ radii of curvature. The eyepiece lens is also a symmetric glass lens. What are the radii of curvature of the eyepiece lens if the telescope鈥檚 magnification is $20 脳$ ?

Short Answer

Expert verified

The radii of curvature of the eyepiece lens is $R_{e y e} = 5 c m$ .

Step by step solution

01

Given Information.

We have given a symmetric glass lens with $100 c m$ radii of curvature.

We need to find the radii of curvature.

02

Calculation.

As we know that:

$M = 20 R_{e y e} = 2 f_{e y e} f_{o b j} = \frac{R}{2} = \frac{100}{2} = 50$

Magnification is related to:

$M = \frac{f_{o b j}}{f_{e y e}} f_{e y e} = \frac{f_{o b j}}{M} f_{e y e} = \frac{50 c m}{20 c m} f_{e y e} = \frac{5}{2} c m$

Here $M$ is magnification, $f_{o b j}$ is the focal length of the object and $f_{e y e}$ is the focal length of the eye.

The radius of the eyepiece $R_{e y e}$ is :

$R_{e y e} = 2 f_{e y e} R_{e y e} = 2 脳 \frac{5}{2} R_{e y e} = 5 c m$

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Most popular questions from this chapter

Ellen wears eyeglasses with the prescription $- 1.0 D$ .

a. What eye condition does Ellen have?

b. What is her far point without the glasses?

A converging lens with a focal length of $40 c m$ and a diverging lens with a focal length of $- 40 c m$ are $160 c m$ apart. A $2 c m$ tall object is $60 c m$ in front of the converging lens.

a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.

b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

A hydrogen discharge lamp emits light with two prominent wavelengths: $656 n m$ (red) and $486 n m$ (blue). The light enters

a flint-glass prism perpendicular to one face and then refracts

through the hypotenuse back into the air. The angle between

these two faces is $35 掳$ .

a. Use Figure $35.18$ to estimate to $卤 0.002$ the index of refraction

of flint glass at these two wavelengths.

b. What is the angle (in degrees) between the red and blue light

as it leaves the prism?

A 2.0-cm-tall object is $20 c m$ to the left of a lens with a focal length of $10 c m$ A second lens with a focal length of $15 c m$ is $30 c m$ to the right of the first lens.

a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.

b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

A $2.0 m$ tall man is $10 m$ in front of a camera with a $15 mm$ focal length lens. How tall is his image on the detector?

See all solutions

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