Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
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
संबंधित प्रश्न
The luminous flux of a 1 W sodium vapour lamp is more than that of a 10 kW source of ultraviolet radiation. Comment.
The sun is less bright at morning and evening as compared to at noon although its distance from the observer is almost the same Why?
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?
As the wavelength is increased from violet to red, the luminosity ____________ .
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 ____________ .
A photographic plate placed a distance of 5 cm from a weak point source is exposed for 3 s. If the plate is kept at a distance of 10 cm from the source, the time needed for the same exposure is _____________ .
A point source of light moves in a straight line parallel to a plane table. Consider a small portion of the table directly below the line of movement of the source. The illuminance at this portion varies with its distance r from the source 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.
Using figure, find the relative luminosity of wavelength (a) 480 nm, (b) 520 nm (c) 580 nm and (d) 600 nm.
The luminous flux of a monochromatic source of 1 W is 450 lumen watt−1. Find the relative luminosity at the wavelength emitted.
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 source emits 31.4 W of radiant flux distributed uniformly in all directions. The luminous efficiency is 60 lumen watt−1. What is the luminous intensity of the source?
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?
A student is studying a book placed near the edge of a circular table of radius R. A point source of light is suspended directly above the centre of the table. What should be the height of the source above the table so as to produce maximum illuminance at the position of the book?
An electric lamp and a candle produce equal illuminance at a photometer screen when they are placed at 80 cm and 20 cm from the screen respectively. The lamp is now covered with a thin paper which transmits 49% of the luminous flux. By what distance should the lamp be moved to balance the intensities at the screen again?
