Question

A telescope has an objective lens of focal length $$150\,cm$$  and an eyepiece of focal length $$5\,cm.$$  If a $$50\,m$$  tall tower at a distance of $$1\,km$$  is observed through this telescope in normal setting, the angle formed by the image of the tower is $$\theta ,$$ then $$\theta $$ is close to:

A. $$6.1\,rad$$
B. $$3.2\,rad$$
C. $$1.5\,rad$$  
D. $$0.2\,rad$$
Answer :   $$1.5\,rad$$
Solution :
Magnifying power of telescope,
$$\eqalign{ & MP = \frac{{\beta \left( {{\text{angle subtended by image at eye piece}}} \right)}}{{\alpha \left( {{\text{angle subtended by object on objective}}} \right)}} \cr & {\text{Also,}}\,\,MP = \frac{{{f_0}}}{{{f_e}}} = \frac{{150}}{5} = 30 \cr & \alpha = \frac{{50}}{{1000}} = \frac{1}{{20}}rad \cr & \therefore \beta = \theta = MP \times \alpha = 30 \times \frac{1}{{20}} = \frac{3}{2} = 1.5\,rad \cr} $$

Releted MCQ Question on
Optics and Wave >> Ray Optics

Releted Question 1

When a ray of light enters a glass slab from air,

A. Its wavelength decreases.
B. Its wavelength increases.
C. Its frequency decreases.
D. neither its wavelength nor its frequency changes.
Releted Question 2

A glass prism of refractive index 1.5 is immersed in water (refractive index $$\frac{4}{3}$$ ). A light beam incident normally on the face $$AB$$  is totally reflected to reach on the face $$BC$$  if
Ray Optics mcq question image

A. $$\sin \theta \geqslant \frac{8}{9}$$
B. $$\frac{2}{3} < \sin \theta < \frac{8}{9}$$
C. $$\sin \theta \leqslant \frac{2}{3}$$
D. None of these
Releted Question 3

A ray of light from a denser medium strike a rarer medium at an angle of incidence $$i$$ (see Fig). The reflected and retracted rays make an angle of $${{{90}^ \circ }}$$ with each other. The angles of reflection and refraction are $$r$$ and $$r’$$ The critical angle is
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A. $${\sin ^{ - 1}}\left( {\tan r} \right)$$
B. $${\sin ^{ - 1}}\left( {\tan i} \right)$$
C. $${\sin ^{ - 1}}\left( {\tan r'} \right)$$
D. $${\tan ^{ - 1}}\left( {\sin i} \right)$$
Releted Question 4

A ray of light from a denser medium strike a rarer medium at an angle of incidence $$i$$ (see Fig). The reflected and retracted rays make an angle of $${{{90}^ \circ }}$$ with each other. The angles of reflection and refraction are $$r$$ and $$r’$$ The critical angle is
Ray Optics mcq question image

A. $${\sin ^{ - 1}}\left( {\tan r} \right)$$
B. $${\sin ^{ - 1}}\left( {\tan i} \right)$$
C. $${\sin ^{ - 1}}\left( {\tan r'} \right)$$
D. $${\tan ^{ - 1}}\left( {\sin i} \right)$$

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