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Please explain with ray diagram
question image
Asked by himanshuneb | 25 Jan, 2019, 11:11: AM
answered-by-expert Expert Answer
Magnification = v/u , where v is the lens to image distance.
Here image of object at infinite distance is formed at focal length , we have v = f.
u is the lens to object distance. For the sake of studying the focal length and aperture effect, let us consider this distance u is constant.
 
Hence if u is constant, magnification is proportional to focal length for the object kept at infinite distance.
 
Hence spot radius  r of sun's image is proportional to focal length f.  Hence πr2 is proportional to f2.
 
except " (B) πr2 begin mathsize 16px style proportional to end style f2  ",  other options are false.

If the lower portion of lens is covered by black paper, still the top portion will view the full size of sun due to infinite distance.
Only the light intensity collected by the lens is halved. Hence we get full image of sun but reduced intensity.
 
By increasing the focal length, magnification increases, hence area of image increases.
If the collecting area of light of the lens is kept constant, intensity decreases by increasing focal length .
This is due to same collecting light intensity by lens,  but image is formed in more area.
Answered by Thiyagarajan K | 25 Jan, 2019, 13:04: PM

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