To Print A Photograph From A Negative, The Time Of Exposure To Light From A Lamp Placed 60  cm Away Is 2.5 S. What Exposure Time Is Required If The Lamp Is Placed 1.2 M Away?

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Question

To print a photograph from a negative, the time of exposure to light from a lamp placed 60  cm away is 2.5 s. What exposure time is required if the lamp is placed 1.2 m away?

Solution

Correct option is

10 s

 

Let I be the luminous intensity of the lamp. The illuminance E1 at a distance r1 (60 cm = 0.60 m) is

                       

If t1 is the exposure time, the total amount of light falling on the negative is

                      

When the lamp is at a distance r2 = 1.2m, the illuminance will be

                     

Let t2 be the exposure time at this distance. The amount of light required is

                    

To obtain the same quality of print, the amount of light falling on the negative must be the same in the two cases, i.e.

                 

Using (i) and (ii) we have

                  

Given r1 = 0.60 mt1 = 2.5 s and r2 = 1.2 m. Hence  

                

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