Advertisements
Advertisements
Question
The illuminance of a small area changes from 900 lumen m−2 to 400 lumen m−2 when it is shifted along its normal by 10 cm. Assuming that it is illuminated by a point source placed on the normal, find the distance between the source and the area in the original position.
Solution
Let the luminous intensity of the source be l and the distance between the source and the area, in the initial position, be x.
Given,
Initial illuminance (EA) = 900 lumen/m2
Final illuminance (EB) = 400 lumen/m2
Illuminance on the initial position is given by,
`E_A=l costheta/x^2............(1)`
Illuminance at final position is given by
`E_B=(lcostheta)/(x+10)^2............(2)`
Equating luminous intensity from (1) and (2), we get
`l=(E_Ax^2)/costheta=(E_B(x+10)^2)/costheta`
`rArr900x^2=400(x+10)^2`
`rArrx/(x+10)=2/3`
⇒ 3x = 2x + 20
⇒ x = 20 cm
The distance between the source and the area at the initial phase was 20 cm.
APPEARS IN
RELATED QUESTIONS
What is the luminous flux of a source emitting radio waves?
Light is incident normally on a small plane surface. If the surface is rotated by an angle of 30° about the incident light, does the illuminance of the surface increase, decreases or remain same? Does your answer change if the light did not fall normally on the surface?
The yellow colour has a greater luminous efficiency as compared to the other colours. Can we increase the illuminating power of a white light source by putting a yellow plastic paper around this source?
An electric bulb is hanging over a table at a height of 1 m above it. The illuminance on the table directly below the bulb is 40 lux. The illuminance at a point on the table 1 m away from the first point will be about ___________ .
Light from a point source falls on a screen. If the separation between the source and the screen is increased by 1%, the illuminance will decrease (nearly) by ____________ .
The intensity produced by a long cylindrical light source at a small distance r from the source is proportional to _________ .
A photographic plate is placed directly in front of a small diffused source in the shape of a circular disc. It takes 12s to get a good exposure. If the source is rotated by 60° about one of its diameter, the time needed to get the same exposure will be ___________ .
Figure shows a glowing mercury tube. The intensities at point A, B and C are related as __________ .
Mark the correct options.
(a) The luminous efficiency of a monochromatic source is always greater than that of a white light source of same power.
(b) The luminous efficiency of a monochromatic source of wavelength 555 nm is always greater than that of a white light source of same power.
(c) The illuminating power of a monochromatic source of wavelength 555 nm is always greater than that of a white light source of same power.
(d) The illuminating power of a monochromatic source is always greater than that of a white light source of same power.
Mark out the correct options.
(a) Luminous flux and radiant flux have same dimensions.
(b) Luminous flux and luminous intensity have same dimensions.
(c) Radiant flux and power have same dimensions.
(d) Relative luminosity is a dimensionless quantity.
A light source emits monochromatic light of 555 nwavelengthm. The source consumes 100 W of electric power and emits 35 W of radiant flux. Calculate the overall luminous efficiency.
A point source emitting 628 lumen of luminous flux uniformly in all directions is placed at the origin. Calculate the illuminance on a small area placed at (1.0 m, 0, 0) in such a way that the normal to the area makes an angle of 37° with the X-axis.
A point source emitting light uniformly in all directions is placed 60 cm above a table-top. The illuminance at a point on the table-top, directly below the source, is 15 lux. Find the illuminance at a point on the table-top 80 cm away from the first point.
Light from a point source falls on a small area placed perpendicular to the incident light. If the area is rotated about the incident light by an angle of 60°, by what fraction will the illuminance change?
Choose the correct answer from given options
Photo diodes are used to detect
Light travels through a glass plate of thickness t and having a refractive index μ. If c is the velocity of light in vacuum, the time taken by the light to travel this thickness of glass is ______.
