Question

A lens having focal length $$f$$ and aperture of diameter $$d$$ forms an image of intensity $$I.$$ Aperture of diameter $$\frac{d}{2}$$ in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively

A. $$f\,{\text{and}}\,\frac{I}{4}$$
B. $$\frac{{3f}}{4}\,{\text{and}}\,\frac{I}{2}$$
C. $$f\,{\text{and}}\,\frac{{3I}}{4}$$  
D. $$\frac{f}{2}\,{\text{and}}\,\frac{I}{2}$$
Answer :   $$f\,{\text{and}}\,\frac{{3I}}{4}$$
Solution :
As we know that
Intensity, $$I \propto A$$   (Area exposed)
$$\eqalign{ & \Rightarrow \frac{{{I_2}}}{{{I_1}}} = \left[ {\frac{{{A_2}}}{{{A_1}}}} \right] = \frac{{\frac{{\pi {d^2}}}{4} - \frac{{\frac{{\pi {d^2}}}{4}}}{4}}}{{\frac{{\pi {d^2}}}{4}}} = \frac{3}{4} \cr & \Rightarrow {I_2} = \frac{3}{4}{I_1} \cr} $$
and focal length remains unchanged.

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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