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(a) Write the expression for the magnification produced by a lens in terms of object distance and image distance.
(b) A $$\begin{aligned}& 4 \\ & \text{cm}\end{aligned}$$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $$\begin{aligned}& 20 \\ & \text{cm}\end{aligned}$$. Calculate the size of the image formed, if the distance of the object from the lens is $$\begin{aligned}& 10 \\ & \text{cm}\end{aligned}$$.
(b) A $$\begin{aligned}& 4 \\ & \text{cm}\end{aligned}$$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $$\begin{aligned}& 20 \\ & \text{cm}\end{aligned}$$. Calculate the size of the image formed, if the distance of the object from the lens is $$\begin{aligned}& 10 \\ & \text{cm}\end{aligned}$$.
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(a) Magnification, $m = \frac{\text{Image distance}}{\text{Object distance}} / m = \frac{v}{u}$
(b)
$h_o= + 4 \text{ cm}$
$f = + 20 \text{ cm}$
$u = -10 \text{ cm}$
$h_i = ?$
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
$\frac{1}{v} = \frac{1}{f} + \frac{1}{u}$
$\frac{1}{v} = \frac{1}{20} + \frac{1}{-10}$
$\frac{1}{v} = \frac{1-2}{20}$
$v = -20 \text{ cm}$
$m = \frac{v}{u}$
$m = \frac{-20}{-10}$
$m = 2$
$m = \frac{\text{height of image}}{\text{height of object}}$
height of image = $m \times$ height of object
height of image = $2 \times 4 \text{ cm} = 8 \text{ cm}$
(b)
$h_o= + 4 \text{ cm}$
$f = + 20 \text{ cm}$
$u = -10 \text{ cm}$
$h_i = ?$
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$
$\frac{1}{v} = \frac{1}{f} + \frac{1}{u}$
$\frac{1}{v} = \frac{1}{20} + \frac{1}{-10}$
$\frac{1}{v} = \frac{1-2}{20}$
$v = -20 \text{ cm}$
$m = \frac{v}{u}$
$m = \frac{-20}{-10}$
$m = 2$
$m = \frac{\text{height of image}}{\text{height of object}}$
height of image = $m \times$ height of object
height of image = $2 \times 4 \text{ cm} = 8 \text{ cm}$