Question 394: Ray Optics

Question

The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m
25
to m
50
. The ratio $${{{m_{25}}} \over {{m_{50}}}}$$ is __________.

Accepted Answer

$${1 \over v} - {1 \over u} = {1 \over f}$$
or, $${u \over v} - 1 = {u \over f}$$
or, $${u \over v} = \left( {{{u + f} \over f}} ight)$$
$$	herefore$$ $$m = {v \over u} = \left( {{f \over {u + f}}} ight)$$
$${{{m_{25}}} \over {{m_{50}}}} = {{\left( {{{20} \over { - 25 + 20}}} ight)} \over {\left( {{{20} \over { - 50 + 20}}} ight)}} = 6$$

Ray Optics

The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m 25 to m 50 . The ratio ${{{m_{25}}} \over {{m_{50}}}}$ is __________.

Integer / Numeric Answer Type