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Multiple choice luminous intensity measurements physics

The luminous intensity of a light source is $500 Cd$. The illuminance of a surface distant $10m$ from it, will be if light falls normally on it

  1. $5$ lux
  2. $10$ lux
  3. $20$ lux
  4. $40$ lux
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Illuminance ($E$)  is  measured  in  lux.  The  lux  is  an  SI  unit  used  when characterizing illumination conditions of a surface:
$E = \dfrac {I}{R^2}     lux$
where $I$ is the luminous intensity and $R$ is the distance.
Given $I = 500 cd$ and $R = 10 m$
$\implies E = \dfrac {500}{10^2} = 5    lux$

Multiple choice luminous intensity measurements physics

A lamp is hanging at a height of $4$ $m$ above a table. The lamp is lowered by $1$ $m$. The percentage increase in illuminance is 

  1. $40$ %
  2. $64$ %
  3. $78$ %
  4. $92$ %
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$Illuminance = illuminating \ power * Cos \theta /d^{2}$


The only change when lamp moves from 4 m to 3 m is its d
Illuminance at 4 m = Power / 16
Illuminance at 3 m = Power / 9

Increase in Illuminance = $\dfrac{power}{9} - \dfrac{power}{16}$ = $ \dfrac{7 Power}{144}$

So % increase = $ \dfrac{7 Power}{144} * \dfrac{16 * 100}{Power}$ = 77.77 % 

Answer. C) 78 %

Multiple choice luminous intensity measurements physics

A photoprint is required to be placed in front of $100$ $Cd$ lamp at a distance of $0.5$ $m$ for $25$ sec for good impression. If it is to be placed in front of a $400$ $Cd$ lamp for $36$ sec for the same impression then the distance of the print from the lamp will be 

  1. $0.5$ $m$
  2. $1.0$ $m$
  3. $1.2$ $m$
  4. $1.5$ $m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the same impression $\dfrac{L * time}{d^{2}}$ has to be constant


Let the required distance be d m
So,
$\dfrac{100 * 25}{0.5^{2}} = \dfrac{400 * 36}{d^{2}}$
=> d = 1.2 m

Answer. C) 1.2 m

Multiple choice luminous intensity measurements physics

Two lamps of luminous intensity of $8$ $Cd$ and $32$ $Cd$ respectively are lying at a distance of $1.2$ $m$ from each other. Where should a screen be placed between two lamps such that its two faces are equally illuminated due to the two sources?

  1. $10$ $cm$ from $8$ $Cd$ lamp
  2. $10$ $cm$ from $32$ $Cd$ lamp
  3. $40$ $cm$ from $8$ $Cd$ lamp
  4. $40$ $cm$ from $32$ $Cd$ lamp
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance between 8 Cd lamp and screen be $ x  m$

Distance between 32 Cd lamp and screen $=$ $ (120-x) m$

Under equal illumination,
$ \dfrac{8}{x^{2}} = \dfrac{32}{(120-x)^{2}}$
=> x $=$ 40 cm

So the distance from 8 Cd lamp is 40 centimeters.

Multiple choice luminous intensity measurements physics

At what distance should a book be placed from a $50 Cd$ bulb so that the illuminance on the book becomes $2lm $ $m^{-2}$

  1. $1$m
  2. $5$m
  3. $10$m
  4. $50$m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Illuminance ($E$)  is  measured  in  lux.  The  lux  is  an  SI  unit 

used  when  characterizing illumination conditions of a surface:
$E = \dfrac {I}{R^2}    lux$
$\implies R = \sqrt {\dfrac {I}{E}}$
where $I$ is the luminous intensity and $R$ is the distance.
Given $I = 50 cd$ and $E = 2 lm  m^{-2}$
$\implies R = \sqrt {\dfrac {50}{2}} = 5   m$

Multiple choice luminous intensity measurements physics

 The luminous flux emitted by the sun will be

  1. $4.4\times10^{25}$ lm
  2. $4.43\times10^{26}$ lm
  3. $4.43\times10^{27}$ lm
  4. $4.43\times10^{28}$ lm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$ luminous \ flux = luminous \ intensity \times solid \ angle$

$ I = 3.53\times 10^{27}$
$ Solid angle  = 4 \pi$

So Luminous flux = $3.53\times10^{27}\times4 \pi$
= $ 4.43\times10^{28} lm$

Answer. D) $ 4.43\times10^{28} lm$

Multiple choice luminous intensity measurements physics

A screen recieves $3$ watt of radiant flux of wavelength $6000$ $\mathring{A}$. One lumen is equivalent to $1.5\times10^{-3}$ watt of monochromatic light of wavelength $5500$ $\mathring{A}$ is $1.00$, then the luminous flux of the source is ___

  1. $4\times10^{3}$ $lm$
  2. $3\times10^{3}$ $lm$
  3. $2\times10^{3}$ $lm$
  4. $1.37\times10^{3}$ $lm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

radiant flux in lumens = $\dfrac{3}{1.5 \times 10^{-3}} = 2000  lm$

relative luminosity at 6000 angstorm is 0.685   
relative luminosity at 5500 angstorm is 1

luminous efficiency  = $\dfrac{0.685}{1}$  

therefore luminous flux = luminous efficiency $\times$ radiant flux = 0.685 $\times$2000 = $1.37 \times 10^3lm$

Multiple choice luminous intensity measurements physics

The luminous intensity of a $100$ W unidirectional bulb is $100$ candela. The total luminous flux emitted from the bulb will be

  1. $100\pi$
  2. $200\pi$
  3. $300\pi$
  4. $400\pi$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We have total luminous flux,
$L = 4 \pi I = 4 \pi \times 100 = 400 \pi$

Multiple choice luminous intensity measurements physics

A point source of $100$candela is held $5$$m$ above a sheet of blotting paper which reflects $75$ % of light incident upon it. The illuminance of blotting paper is 

  1. $4$ phot
  2. $4$ lux
  3. $3$ phot
  4. $3$ lux
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Illuminance = $\dfrac{L}{d^{2}}$
$\dfrac{100}{5^{2}}$ = 4 lux

Answer. B) 4 lux
Multiple choice luminous intensity measurements physics

Inverse square law for illuminance is valid for 

  1. isotropic point source

  2. cylindrical source

  3. search light

  4. all types of sources
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Inverse square law for illuminance is valid and can be applied for all types of sources.