\(Height\ of\ the\ object\ =2cm\\ Object\ distance(u)=-20cm\\ Focal\ length(f)=12cm\\ \frac { 1 }{ v } +\frac { 1 }{ -20 } =\frac { 1 }{ -12 } \\ \frac { 1 }{ v } -\frac { 1 }{ -20 } =\frac { 1 }{ -12 } \\ \frac { 1 }{ v } =\frac { -3+5 }{ -60 } +\frac { 2 }{ 60 } \\ The\ image\ distance=30cm\\ Height\ of\ the\ object=2cm\\ m=\frac { { h }_{ 1 } }{ { h }_{ 0 } } -\frac { v }{ u } \\ =\frac { 30 }{ 20 } =\frac { -v }{ 2 } =\frac { 30\times 2 }{ 20 } =3\\ Height\ of\ the\ imageis=3cm\\ so\ it\ is\ a\ real,\ invented\ and\ magnified\ image.\)

Between the focus F and the pole P of the mirror.

 Position of Image        Size of Image        Nature of Image
​​​​​​Behind the mirror          Magnified               Virtual and Erect.

a) Rarer to denser medium:
When a ray of light travels from optically rarer medium to optically denser medium, it bends towards the normal.

b) Denser medium to rarer medium:
When a ray of light travels from an optically denser medium to an optically rarer medium it bends away from the normal.

c) Normal to the surface separating the two media:
A ray of light incident normally on a denser medium goes without any deviation.

\(\frac { 1 }{ f } =\frac { 1 }{ u } +\frac { 1 }{ v } \)
\(\frac { 1 }{ 20 } =\frac { 1 }{ -600 } +\frac { 1 }{ v } \)
\(\frac { 1 }{ v } =\frac { 1 }{ 20 } -\frac { 1 }{ -600 } \)
= \(\frac { 1 }{ 20 } +\frac { 1 }{ 600 } \)
\(\frac { 1 }{ v } =\frac { 30+1 }{ 600 } =\frac { 31 }{ 600 } \)
\(v=\frac { 600 }{ 31 } \)
= 19.35 cm
b) Size of the image
\(m=\frac { -v }{ u } \)
= \(-\frac { v }{ (-u) } =\frac { -600 }{ 31 } \times \frac { 1 }{ -600 } \)
m=\(\frac { 1 }{ 31 } \)
Breadth of image =\(\frac { 1 }{ 31 } \)\(\times\)200 cm= 6.45 cm
Height of image = \(\frac { 1 }{ 31 } \) \(\times\)160 cm= 5.16 cm

Refractive index of glass = 1.5
Speed of light in vacuum = 3 x 10⁸ ms^-1
Speed of light in glass = ?
\(c = \frac {\text{Speed of light in vacuum}}{\text{Speed of light in glass}}\)
\(\text{Speed of light in glass } = \frac {\text{Speed of light in vacuum}}{\text{Refractive index of glass}}\)
\(= \frac {3\times10^8}{1.5} =2\times 10^8 ms^-1\)