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a screen is placed a distance 40 cm away from an illuminated object.a converging lens is placed between the source and the screen and it is attempted to form the image of the source on the screen. if no position could be found, the focal lenth of lens.
A)must be less than 10 cm
B)must be gretaer than 20 cm
C)must not be greater than 20cm
​D) must not be less than 20 cm
Give detailed answer

bal krishna , 10 Years ago
Grade 12
anser 2 Answers
Mallikarjun Maram
None of the answers is correct.
Last Activity: 10 Years ago
Debomoy Roy
Let, an image is formed in the screen. 
Let, object distance = u
therefore, Image distance, v = 40 – u
Now, from lens formula 
we have, 
      1/v – 1/u = 1/f
=> 1/(40 – u) – 1/(-u) = 1/fmin
=> 1/(40-u) + 1/u = 1/fmin      ….....(i)
Differentiating with respect to ‘u’ ,
=> d/du{1/(40-u)}+ d/du {1/u) = d/du{1/fmin}
=>(40-u)-2 - u-2 = – f-2 d/du {fmin}
=> (40-u)-2- u-2 = 0     [since d/du {fmin} = 0]
=>(40-u)-2= u-2
=> 1/(1600 – 80u + u2) = 1/u2
=>80u = 1600
=> u = 20 
 (i)=> 1/20 + 1/(40-20) = 1/fmin
   =>fmin = 10 
Therefore, the minimum focal length is 10 when the image is form. 
But according to question the image can’t be form, so the focal length of the image must be greater than 10 .
 
 
Last Activity: 8 Years ago
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