Question

An object 5.0 cm in length is placed at a distance of 20cm in front of a convex mirror of radius of curvature 30cm. Find the position of the image its nature and size ?


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Answer 1

Size of object = 5.0cm

Distance = -20cm

Radius = 30cm

Position = ?

Size = ?

Apply Mirror Formula :-

= $\bf\huge\frac{1}{u} + \frac{1}{v} = \frac{2}{R}$

= $\bf\huge\frac{1}{v} = \frac{2}{R} - \frac{1}{u}$

= $\bf\huge\frac{2}{30} - \frac{1}{-20}$

= $\bf\huge\frac{1}{15} + \frac{1}{20}$

= $\bf\huge\frac{1}{v} = \frac{7}{60}$

$\bf\huge => v = \frac{60}{7} = 8.6cm$

Magnification => $\bf\huge - \frac{v}{u} = \frac{-8.6}{-20} = 0.43$

=> $\bf\huge\frac{Size\: of\: Image}{Size\: of\: object} = Magnification$

=> $\bf\huge\frac{Size\:of\:Image}{5.0cm} = 0.43$

Size of Image = 0.43 × 5.0

Size of Image = 2.2cm