Thin lenses. Object O stands on the central axis of a thin symmetric lens. For t

Question

Thin lenses. Object O stands on the central axis of a thin symmetric lens. For this situation, each problem in the table (below) gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of the lens as object O or on the opposite side.

Explanation / Answer

Given that distance of the object from the lens is p = 23 cm
focal length of diverging lens is f = -15 cm
a) Image distance
from the lens makers formula 1/ f = 1/ p + 1/ q
1/ -15 = 1/ 23cm + 1/ q
q = -9.07 cm
b) lateral magnification is m = - q / p
= - (-9.07cm) / 23cm
= 0.39
c) As the image disance is negative it is virtual
d) As the magnification is + ve it is non inverted
e) As the image distance is negative the image is formed as the same side of the lens
Note : If the lens is converging focal length is positive
If the lens is diverging the lens is negative
As the image distance is negative the image is formed at the same side of the lens
If the magnification is positive the image is non inverted

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