Question

If a mark of size $0.2cm$ on the surface of a glass sphere of diameter $10cm$ and $\mu =1.5$ is viewed through the diametrically opposite point, where will the image be seen and of what size ?

Answer 1

As the mark is on surface, refraction will take place on the other surface only.

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_1-{\mu }_2}{R}$

$\frac{1}{v}-\frac{1.5}{-10}=\frac{1.5-1}{-5}$

$\frac{1}{v}=\frac{-5}{100}$

$v=-20cm$

The image will be at a distance20 cm from point P toward O.

Ref. image

Magnification $M=\frac{I}{O}=\left(\frac{v}{u}\right)\left(\frac{{\mu }_1}{{\mu }_2}\right)$

$=\left(\frac{-20}{-10}\right)\left(\frac{15}{1}\right)$

$m=3$

$I=3\times 0.2$

$=0.6cm$

Image will be enlarged & virtual.