A needle 4 cm high is placed in front of a lens. Image of the needle is real, inverted and 6 cm high, when the distance between the needle and its image is 20 cm. find the focal length of lens and also write the type of the lens. Draw the ray diagram also.
CBSE, class XIII guys.
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h = 4 cm h' = - 6 cm m = -6/4 = - 1.5
Since image is magnified, inverted real, it is a convex lens.
| u | + v = 20 cm v - u = 20 cm as u is -ve.
m = v / u => v = - 1.5 u
- 1.5 u - 1 u = 20 => u = - 20/2.5 = - 8 cm
v = +12 cm
1/v - 1/u = 1/f => 1/12 + 1/8 => f = 24/5 = 4.8 cm
Since image is magnified, inverted real, it is a convex lens.
| u | + v = 20 cm v - u = 20 cm as u is -ve.
m = v / u => v = - 1.5 u
- 1.5 u - 1 u = 20 => u = - 20/2.5 = - 8 cm
v = +12 cm
1/v - 1/u = 1/f => 1/12 + 1/8 => f = 24/5 = 4.8 cm
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