A convex mirror has a focal length of -5cm. An object with a height of 4cm is 3cm from the mirror. Calculate the image distance.

Expert Answers

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To solve for the image distance, apply  the equation for curved mirrors which is:

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

where `d_o` - object distance, `d_i` - image distance and `f ` - focal length.

Substitute f = -5 cm and `d_o` = 3 cm to the formula above.

`1/3 + 1/d_i=1/-5`

To simplify, multiply both sides by the LCD which is 15d.

`15d_i*(1/3+1/d_i)=(1/-5)*15d_i`

`5d_i + 15 = -3d_i`

Bring together the terms with `d_i` . 

`5d_i - 5d_i + 15= -3d_i - 5d_i`

`15=-8d_i`

Then, isolate `d_i` . 

`15/-8 = (-8d_i)/(-8)`

`-1.875=d_i`

Hence, the image distance is -1.875 cm.

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