Question

A linear aperture whose width is $$0.02\,cm$$  is placed immediately in front of a lens of focal length $$60\,cm.$$  The aperture is illuminated normally by a parallel beam of wavelength $$5 \times {10^{ - 5}}cm.$$   The distance of the first dark band of the diffraction pattern from the centre of the screen is

A. $$0.10\,cm$$
B. $$0.25\,cm$$
C. $$0.20\,cm$$
D. $$0.15\,cm$$  
Answer :   $$0.15\,cm$$
Solution :
1st minima is formed at a distance $$Y = \frac{{\lambda D}}{a}$$
For the distance of the first dark band of the diffraction pattern from the centre of the screen is given by position of 1st minima.
i.e. $$Y = \frac{{\lambda D}}{a}$$
where, $$\lambda =$$  wavelength of parallel beams
$$D =$$  focal length
$$a =$$  width of linear aperture.
$$\eqalign{ & \Rightarrow Y = \frac{{\left( {5 \times {{10}^{ - 5}}} \right)\left( {0.6} \right)}}{{0.02 \times {{10}^{ - 2}}}}\,\,\left( {{\text{given}}} \right) \cr & \Rightarrow Y = 0.15\,cm \cr} $$

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.
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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
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A. $$\sin \theta \geqslant \frac{8}{9}$$
B. $$\frac{2}{3} < \sin \theta < \frac{8}{9}$$
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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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