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CBSE Class 10 Science 2023 Delhi Set 1

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Question : 31 of 39
Marks: +1, -0
The power of a lens is +4D+4 D. Find the focal length of this lens. An object is placed at a distance of 50cm50 \mathrm{cm} from the optical centre of this lens. State the nature and magnification of the image formed by the lens and also draw a ray diagram to justify your answer.
Solution:  
Focal length =1P=14=0.25m= \frac{1}{P} = \frac{1}{4} = 0.25 \mathrm{m} or 25cm25 \mathrm{cm}. It is a convex lens as power and focal length are positive.
Focal length, f=+25cmf = +25 \mathrm{cm}
Object distance, u=−50cmu = -50 \mathrm{cm}
Image distance, v=v = ?
Image height, I=I = ?
Using lens formula,   1f=  1v−  1u\; \frac{1}{f} = \; \frac{1}{v} - \; \frac{1}{u}
  125=  1v−  1−50\; \frac{1}{25} = \; \frac{1}{v} - \; \frac{1}{-50}
  1v=  125−  150\; \frac{1}{v} = \; \frac{1}{25} - \; \frac{1}{50}
v  =+50cmv \; = +50 \mathrm{cm}
Also, magnification, m=−vum = - \frac{v}{u}
Hence,     m=50−50=−1\; \; m = \frac{50}{-50} = -1
Hence, image is formed at 50cm50 \mathrm{cm} in front of the lens. The image is of the same size as the object as magnification is 1 . The negative magnification shows that image is inverted.
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