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A paper, with two marks having separation d, isheld normal to the line of sight of an observer ata distance of 50m. The diameter of the eye-lensof the observer is 2 mm. Which of the followingis the least value of d, so that the marks can beseen as separate ? The mean wavelength ofvisible light may be taken as 5000 Å.     [2002]
  • a)
    1.25 m
  • b)
    13.6 cm
  • c)
    12.5 cm
  • d)
    2.5 mm
Correct answer is option 'C'. Can you explain this answer?

Gowri Nair answered
Angular limit of resolution of eye, 
where, d is diameter of eye lens.
Also, if y is the minimum separation between two objects at distance D from eye then
θ = y/D
Here, wavelength λ = 5000Å = 5x10-7m
D = 50 m
Diameter of eye lens = 2 mm = 2x10-3 m
From eq. (1), minimum separation is
y = 5 * 10-7 * 50 / 2 * 10-3
y = 0.0125 m
y = 1.25 cm

The periodic waves of intensities I1 and I2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:
  • a)
    I1 + I2
  • b)
  • c)
  • d)
    2(I1+ I2)
Correct answer is option 'D'. Can you explain this answer?

Tejas Chavan answered
The resultant intensity of two periodic
waves at a point is given by
Resultant intensity is maximum if
Resultant intensity is minimum if
Therefore, the sum of the maximum and
minimum intensities is Imax + Imin

Colours appear on a thin soap film and on soapbubbles due to the phenomenon of [1999]
  • a)
    refraction
  • b)
    dispersion
  • c)
    interference
  • d)
    diffraction
Correct answer is option 'C'. Can you explain this answer?

Devansh Mehra answered
We know that the colours for which the
condition of constructive interference is
satisfied are observed in a given region of the film. The path difference between the light waves reaching the eye changes when the position of the eye is changed. Therefore, colours appear on a thin soap film or soap bubbles due to the phenomenon of interference.

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