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Find the distance of object form a conca...

Find the distance of object form a concave morror of focal length 10 cm so that image size is four times the size of the object.

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The correct Answer is:
A, B, C
Concave mirror can form real as well as virtual image, Here, nature of image is mot given in the question so, we will consider two possible cases.
Case 1(When image is real ) Real image is forned on the same side of the object ,i.e. U,v, and f all are nagative.so let,
` u=-x`
`then v=-4x as |(v/u)|=|m|=4`
and `f=-10cm`
Sunstituting in `(1/v)+(1/u)=(1/f)`,
We have `(1/(-4x))+(1/x)=(1/(-10))`, or `(5)/(4x)=1/10`
`:. x=12.5 cm`
case2 (When image is virtual ) In case of a mirro, image is virtual, when it is formed behind the mirror, i.e u and f are negative while v is positive. So let,
`u=-y`
then `v= +4y `and `f= -10 cm`
Substituting in `1/v+1/u=1/f`
we have `1/(4y)-(1/y)=(1/(-10))`
or, `(3/4y)=(1/10)`
or, `y=7.5 cm`.
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