Question

If an object is 30cm in front of a convex mirror that has a focal length of 60cm, how far behind the mirror will the image appear to an observer? How tall will the image be?

Answer 1

Given :-

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• Focal length = 60cm
• Distance btw. mirror and object = v = 30cm

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To find :-

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• How far behind the mirror will the image appear to an observer?
• How tall will the image be?

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Solution :-

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Since , the mirror is a convex mirror

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Focal length = + 60 cm

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u = - 30cm ( since the object will be placed on the negative side )

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Now ;

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Distance btw. the image and mirror = + v ( since it is given that image will be formed behind the mirror )

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Acc. to the mirror formulae ;

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$\sf{\star{\large{\boxed{\purple{\mathsf{ \dfrac{1}{f} = \dfrac{1}{u}+ \dfrac{1}{v}}}}}}}$

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$\sf \implies \dfrac{1}{60} = \dfrac{1}{-30} + \dfrac{1}{v}$

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$\sf \implies \dfrac{1}{v} = \dfrac{ 1 }{60} + \dfrac{1}{30}$

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$\sf \implies \dfrac{1}{v} = \dfrac{1 + 2 }{60}$

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$\sf \implies \dfrac{1}{v} = \dfrac{3}{60}$

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$\sf \implies \dfrac{1}{v} = \dfrac{1}{20}$

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$\sf \implies v = 20 cm$

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$\sf{\dag{\large{\boxed{\orange{\bold{Image\: will \: be \: formed \: 20cm \: behind \:the \: mirror }}}}}}$

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We know that ;

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$\sf{\star{\large{\boxed{\purple{\mathrm{ Magnification = - \dfrac{ v }{u}}}}}}}$

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Therefore ;

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Magnification = - ( -20 ) / 30

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Magnification = 20 / 30

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Magnification = 2 / 3

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$\sf{\dag{\large{\boxed{\orange{\bold{Image\: will \: be \: small \: in \: size \:in \: ratio \: 2 : 3 }}}}}}$

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Answer :-

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• Image will be formed 20 cm behind the mirror
• Image will be smaller in size then the object by 0.67x