Question

A convex lens is in contact with concave lens. The magnitude of the ratio of their focal length is $$\frac{2}{3}.$$ Their equivalent focal length is $$30\,cm.$$  What are their individual focal lengths?

A. $$ - 15, 10$$  
B. $$ - 10, 15$$
C. 75, 50
D. $$ - 75, 50$$
Answer :   $$ - 15, 10$$
Solution :
$$\frac{{\left| {{f_1}} \right|}}{{\left| {{f_2}} \right|}} = \frac{2}{3}$$
$${{f_1}}$$ : focal length of convex lens.
$$\eqalign{ & \frac{1}{f} = \frac{1}{{{f_1}}} - \frac{1}{{{f_2}}} \cr & \Rightarrow \,\,\frac{1}{{30}} = \frac{1}{{{f_1}}} - \frac{2}{{3{f_1}}} \cr & {f_1} = 10\,cm,{f_2} = - 15\,cm \cr} $$

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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