Question

A convex lens forms an image at 36cm when an object is placed at 18cm from the lens.
what is the focal length of the lens? what will be the height of the image if the object has
3cm height? draw a ray diagram with a proper scale{hint take scale 6cm=1cm}

Answer 1

Answer:

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Explanation:

$to \: find = \\1. focal \: length \: (f) \\ 2.height \: of \: image \: (h2) \\ \\ given = \\ for \: a \: convex \: lens \\ height \: of \: object \: (h1) = 3.cm \\ object \: distance \: (u) = - 18.cm \\ image \: distance \: (v) = 36.cm \\ \\ so \: thus \: applying \: lens \: formula \\ \\ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \\ \\ \frac{1}{f} = \frac{1}{36} - \frac{1}{( - 18)} \\ \\ = \frac{1}{36} + \frac{1}{18} \\ \\ = \frac{36 + 18}{(36 \times 18)} \\ \\ = \frac{54}{648} \\ \\ = \frac{1}{12} \\ \\ applying \: invertendo \\ f = 12.cm$

$so \: we \: know \: that \\ \\ \frac{h2}{h1} = \frac{v}{u} \\ \\ \frac{h2}{3} = \frac{36}{( - 18)} \\ \\ = \frac{h2}{3} = - 2 \\ \\ h2 = - 2 \times 3 \\ \\ h2 = - 6.cm \\ \\ here \: negative \: sign \: indicates \: that \\ image \: is \: real \: and \: inverted \: and \: is \: \\ formed \: below \: principal \: axis$