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Magnification of Reflecting Telescope in Normal Adjustment

Normal Adjustment of Reflecting Telescope

A reflecting telescope is said to be in normal adjustment when:
  • The final image is formed at infinity
  • The observer’s eye is relaxed
  • The image formed by the objective mirror lies at the focal plane of the eyepiece

Ray Diagram of Reflecting Telescope (Normal Adjustment)

For construction and working, refer to:
https://edulodhi.in/reflecting-telescope/ Magnification of reflecting telescope in normal adjustment ray diagram

Definition of Magnifying Power

The magnifying power of a telescope is defined as the ratio of the angle subtended by the final image at the eye to the angle subtended by the object when seen directly. $[ M = \dfrac{\beta}{\alpha} ]$

Derivation of Magnification of Reflecting Telescope

Let ( f_o ) = focal length of objective mirror ( f_e ) = focal length of eyepiece ( h ) = height of image formed by objective

Step 1: Angle Subtended by the Object

For a distant object, the image is formed at the focus of the objective mirror. $[ \alpha = \dfrac{h}{f_o} ]$

Step 2: Angle Subtended by the Final Image

The eyepiece acts as a magnifier. $[ \beta = \dfrac{h}{f_e} ]$

Step 3: Magnifying Power

$[ M = \dfrac{\beta}{\alpha} = \dfrac{h/f_e}{h/f_o} ]$ $[ \boxed{M = -\dfrac{f_o}{f_e}} ]$

Final Formula

$[ \boxed{\text{Magnification of reflecting telescope in normal adjustment} = -\dfrac{f_o}{f_e}} ]$

Meaning of Negative Sign

The negative sign indicates that the final image formed by the reflecting telescope is inverted.

Factors Affecting Magnification

The magnifying power of a reflecting telescope depends on:
  • Focal length of objective mirror
  • Focal length of eyepiece
It does not depend on the aperture of the mirror.

Solved Numerical

A reflecting telescope has an objective of focal length 150 cm and an eyepiece of focal length 5 cm. Find its magnifying power in normal adjustment. $[ M = -\dfrac{150}{5} = -30 ]$ Magnifying power = 30

Assertion–Reason Questions

Q1. Assertion (A): In normal adjustment of a reflecting telescope, the final image is formed at infinity. Reason (R): The intermediate image lies at the focal plane of the eyepiece. A. Both A and R are true and R explains A B. Both A and R are true but R does not explain A C. A is true, R is false D. A is false, R is true Correct Answer: A
Q2. Assertion (A): Increasing the focal length of the eyepiece decreases the magnifying power of a reflecting telescope. Reason (R): Magnifying power is inversely proportional to the focal length of the eyepiece. A. Both A and R are true and R explains A B. Both A and R are true but R does not explain A C. A is true, R is false D. A is false, R is true Correct Answer: A
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