Q: A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below . Correct shape of the emergent wavefront will be
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Q: A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below . Correct shape of the emergent wavefront will be
Q: A man wants to distinguish between two pillars located at a distance of 11 km. What should be the minimum distance between the pillars ?
Sol: As the limit of resolution of human eye is
$\displaystyle \theta = 1′ = (\frac{1}{60})^o $
$\displaystyle \theta = \frac{\pi}{60 \times 180} $
If x is minimum distance between the pillars,
and d = 11 km = 11 × 103 m ,
then from $\displaystyle \theta = \frac{x}{d} $
$\displaystyle x = d \times \theta $
$\displaystyle x = 11 \times 10^3 \times \frac{\pi}{60 \times 180} $
x = 3.2 m
Q: Two beams, A and B of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity. (and beam B has zero intensity), a rotation of polaroid through 30° makes the two beams appear equally bright. If the initial intensities of the two beams are IA and IB respectively, then IA/IB equals.
(a) 1
(b) 1/3
(c) 3
(d) 3/2
Sol: As IA and IB are initial intensities, therefore, on rotation of polaroid through 30°,
IA‘ = IA cos230°
IB‘ = IB cos260°
As IA‘ = IB‘
IA cos230° = IB cos260°
$\displaystyle \frac{I_A}{I_B} = \frac{cos^2 60^o}{cos^2 30^o} $
$\displaystyle \frac{I_A}{I_B} = \frac{1/4}{3/4} $
$\displaystyle \frac{I_A}{I_B} = \frac{1}{3} $
Q: A beam of light λ = 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is
(a) 1.2 cm
(b) 1.2 mm
(c) 2.4 cm
(d) 2.4 mm
$\displaystyle 2 x = \frac{2 \lambda D}{a} $
$\displaystyle 2 x = \frac{2 \times 6 \times 10^{-7}\times 2}{10^{-3}} $
$\displaystyle 2 x = 2.4 \times 10^{-3}m = 2.4 mm $