relation between intensity of image and aperture when half of the lens is covered

Asked by kathyvincent11 | 1st Jun, 2020, 04:40: PM

Expert Answer:

When the half of the lens is covered then the intensity of image decreases. 
 
This is because the intensity of the image is directly proportional to the area of aperture of lens receiving the light. 
The area of aperture is given as, 
 
A equals space 2 pi r squared space
T h i s space c a n space a l s o space b e space w r i t t e n space a s comma space
A equals space fraction numerator pi d squared over denominator 4 end fraction space
W h e n space t h e space h a l f space l e n s space i s space c o v e r e d comma space
h a l f space o f space t h e space d i a m e t e r space o f space l e n s space i s space c o v e r e d
T h u s comma space a r e a space o f space a p e r t u r e space w h e n space h a l f space l e n s space i s space c o v e r e d space i s space
A apostrophe space equals fraction numerator pi d squared over denominator 4 end fraction space minus space fraction numerator pi open parentheses begin display style d over 2 end style close parentheses squared over denominator 4 end fraction space space equals space fraction numerator pi d squared over denominator 4 end fraction space minus space fraction numerator pi d squared over denominator 16 end fraction space equals space space fraction numerator 3 pi d squared over denominator 16 end fraction space

T h u s comma space i n t e n s i t y space o f space i m a g e space i s comma space
fraction numerator I over denominator I apostrophe end fraction space equals space fraction numerator A over denominator A apostrophe end fraction space equals space fraction numerator fraction numerator pi d squared over denominator 4 end fraction space over denominator fraction numerator 3 pi d squared over denominator 16 end fraction space end fraction space equals space 4 over 3
I apostrophe space equals space 3 over 4 I space space

H e n c e comma space t h e space i n t e n s i t y space o f space t h e space i m a g e space r e d u c e s space b y space 3 divided by 4 space t i m e s space t h e space o r i g i n a l space v a l u e space w h e n space t h e space h a l f space l e n s space i s space c o v e r e d space

Answered by Shiwani Sawant | 1st Jun, 2020, 08:13: PM