Question

Two thin lenses of focal lengths $${f_1}$$ and $${f_2}$$ are in contact and coaxial. The power of the combination is

A. $$\sqrt {\frac{{{f_1}}}{{{f_2}}}} $$
B. $$\sqrt {\frac{{{f_2}}}{{{f_1}}}} $$
C. $$\frac{{{f_1} + {f_2}}}{2}$$
D. $$\frac{{{f_1} + {f_2}}}{{{f_1}{f_2}}}$$  
Answer :   $$\frac{{{f_1} + {f_2}}}{{{f_1}{f_2}}}$$
Solution :
As and we know that $${P_{{\text{eq}}}} = {P_1} + {P_2}$$
$$\eqalign{ & \frac{1}{{{F_{{\text{eq}}}}}} = \frac{1}{{{f_1}}} + \frac{1}{{{f_2}}} \cr & \therefore {F_{{\text{eq}}}} = \frac{{{f_1}{f_2}}}{{{f_1} + {f_2}}} \cr & {\text{As}}\,\,P = \frac{1}{F} \cr & \therefore {P_{{\text{eq}}}} = \frac{{{f_1} + {f_2}}}{{{f_1}{f_2}}} \cr} $$

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
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. $${\tan ^{ - 1}}\left( {\sin i} \right)$$
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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