Question #169953

An object is 0.25 m from a concave mirror with a focal length of 0.6 m the object is 0.38 m talk.


1
Expert's answer
2021-03-08T08:09:56-0500

Given,

Object distance (u) = 0.25m

Focal length of the concave mirror (f)=0.6m(f)=0.6m

Length of the object (ho)=0.38m(h_o)=0.38m

Let position of image be at v distance from the concave mirror.

Now, applying the mirror formula,

1v+1u=1f\frac{1}{v}+\frac{1}{u}=\frac{1}{f}

Now, substituting the values,

1v=1f1u\frac{1}{v}=\frac{1}{f}-\frac{1}{u}

for the concave mirror, focal length always will be negative. so

1v=10.610.25\frac{1}{v}=\frac{1}{0.6}-\frac{1}{0.25}


1v=0.250.60.150\Rightarrow \frac{1}{v}=\frac{0.25-0.6}{0.150}


1v=0.350.15\Rightarrow \frac{1}{v}=\frac{-0.35}{0.15}

v=37cmv=\frac{-3}{7}cm

Hence the height of the image hi=ho×vu=3×0.387cmh_i=\frac{-h_o\times v}{u}=\frac{3\times 0.38}{7}cm

hi=1.147cm=0.16cmh_i=\frac{1.14}{7}cm =0.16cm


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