Question

An object is 24 cm away from a concave mirror and its image is 16 cm from the mirror. Find the focal length and radius of curvature of the mirror, and the magnification of the image.

Answer 1

Distance of object (u) = -24 cm
Distance of image (v) = -16 cm
We have to find the focal length of the mirror (f) and the magnification of the image (m).
Using the mirror formula, we get  

`1/f=1/u+1/v` 

`1/f=1/-24+1/-16` 

`or 1/f=(-2-3)/48` 

`or 1/f=(-5)/48` 

`or f=-48/5` 

`f=-9.6` cm 

Therefore, the focal length of the concave mirrio is 9.6 

R adius of curvature (R)=2f 

   `R=2xx-9.6` 

   `R=-19.2 cm` 

Therefore, the radius of curvature of the mirror is 19.2 cm 

Now, using the magnification formula, we get 

`m =(-v)/u` 

`m=(-16)/-24` 

m=0.66 

Thus, the image is real, inverted and small in size.