Given, The focal length of a convex lens, f = 18 cm. Image distance, v = 24 cm Object distance, u = ? To find- Magnification Solution: By using lens formula- $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\phantom{\rule{0ex}{0ex}}$ where, v = image distance, u = object distance, and f = focal length Substituting the values of f, v and u we get, $\frac{1}{24}-\frac{1}{u}=\frac{1}{18}\phantom{\rule{0ex}{0ex}}$ $\frac{1}{24}-\frac{1}{18}=\frac{1}{u}\phantom{\rule{0ex}{0ex}}$ $\frac{18-24}{24\times 18}=\frac{1}{u}\phantom{\rule{0ex}{0ex}}$ $\frac{6}{24\times 18}=\frac{1}{u}\phantom{\rule{0ex}{0ex}}$ $\frac{1}{4\times 18}=\frac{1}{u}\phantom{\rule{0ex}{0ex}}$ $u=-72cm\phantom{\rule{0ex}{0ex}}$ So, the object distance is -72cm. The object should be placed at a distance of -72 cm from the lens. Now, the equation for finding magnification of a lens can be given as- $m=\frac{v}{u}\phantom{\rule{0ex}{0ex}}$ Substituting the values in magnification formula we get- $m=\frac{24}{-72}\phantom{\rule{0ex}{0ex}}$ $m=-\frac{1}{3}\phantom{\rule{0ex}{0ex}}$ Hence, the magnification produced will be $m=-\frac{1}{3}\phantom{\rule{0ex}{0ex}}$ At what distance should an object be placed from a lens of focal length 25 cm to obtain its image on a screen placed on the other side at a distance of 50 cm from the lens? What will be the magnification produced in this case? Given that, Focal length, f = 25 cm Image distance, v = 50 cm Form the lens formula, `1/v-1/u=1/f` (where u = object distance) `"or", 1/u=1/v-1/f` `=1/50-1/25` Therefore, `1/u=(-1)/50` Or, u = −50 cm Magnification, `m=v/u` `=50/(-50)` = -1
The object must be placed 50 cm away from the lens, on the other side to produce a magnification of −1. Concept: Magnification Due to Spherical Lenses Is there an error in this question or solution? |