## A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below . …

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

Click to See Solution :
Ans: (a)
Sol:

## A man wants to distinguish between two pillars located at a distance of 11 km. What should be the minimum distance between the pillars?

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

## Two beams, A and B of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid…..

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

Ans: (b)

Sol: As IA and IB are initial intensities, therefore, on rotation of polaroid through 30°,

IA‘ = IA cos2⁡30°

IB‘ = IB cos2⁡60°

As IA‘ = IB

IA cos2⁡30° = IB cos2⁡60°

$\displaystyle \frac{I_A}{I_B} = \frac{cos^2 60^o}{cos^2 30^o}$

$\displaystyle \frac{I_A}{I_B} = \frac{1/4}{3/4}$

$\displaystyle \frac{I_A}{I_B} = \frac{1}{3}$

## A beam of light λ = 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern ….

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

$\displaystyle 2 x = \frac{2 \lambda D}{a}$
$\displaystyle 2 x = \frac{2 \times 6 \times 10^{-7}\times 2}{10^{-3}}$
$\displaystyle 2 x = 2.4 \times 10^{-3}m = 2.4 mm$