The focal length of a concave mirror is 30cm. Find the position of the object infront of the mirror so that the virtual image is three times the size of the object.Please answer.... its...

The focal length of a concave mirror is 30cm. Find the position of the object infront of the mirror so that the virtual image is three times the size of the object.Please answer.... its urgent...thank you

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Since the virtual image is 3 times the height of the size of the object, then `h_i=3h_0` , where `h_i` is the image height and `h_o` is the object's height.

Base on this, the magnification factor (m) of the mirror is:

`m=h_i / h_o = (3h_o)/h_o=3`

Moreover, magnification factor is equal to the negative ratio of image distance (`d_i` )  and object's distance (`d_o` ) from the mirror.

`m=-d_i / d_o`

`3=-d_i /d_o`

Expressing `d_i` in terms of `d_o` result to:

`d_i=-3d_o`

Then, apply the mirror equation to solve for `d_o` .

`1/d_o + 1/d_i = 1/f`

Substitute `d_i=-3d_o`  and f=30 cm to the formula.

`1/d_o + 1/(-3d_o) = 1/30`

`1/d_o - 1/(3d_o)=1/30`

To simplify the equation, multiply both sides by the LCD which is 30d_o.

`30d_o*(1/d_o - 1/(3d_o))=1/30*30d_o`

`30 - 10=d_o`

`20 =d_o`

Hence, the object is placed at a distance of 20 cm from the concave mirror.

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