

$\text{p}=\frac{1}{\text{f}}$
So, $\frac{1}{0.1}=10\text{D}$$\text{p}_2=\frac{1}{0.2}=5\text{D}$
Since $\text{p}_1>\text{p}_2$ So the lens with focal length 10cm has greater convergence of refracted light.
$\frac{1}{\text{v}}-\frac{1}{\text{u}}=\frac{1}{\text{f}}$
This is the lens formula. The lens formula has a minus sign (-) between $\frac{1}{\text{v}}$ and $\frac{1}{\text{u}}$ wheres the mirror formula has a plus sign (+) between $\frac{1}{\text{v}}$ and $\frac{1}{\text{u}}$$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\text{m}=\frac{\text{v}(\text{distance of image})}{\text{u}(\text{distance of object})}$
Magnification fomula for a mirror has a minus sign (-) but the Magnification fomula for a lens has to minus sign. Magnification fomula for a mirror is:$\text{m}=-\frac{\text{v}(\text{distance of image})}{\text{u}(\text{distance of object})}$
$\text{Magnification (m)} = \frac{\text{height of image}}{\text{height of object}} = \frac{\text{h}'}{\text{h}}$
$\text{Magnification (m)} = −\frac{\text{image distance}} {\text{object distance}} =\frac{\text{v}}{\text{u}}$







$\frac{1}{\text{v}}+\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\Rightarrow\frac{1}{(-10)}+\frac{1}{(-15)}=\frac{1}{\text{f}}$
$\Rightarrow\frac{1}{\text{f}}=\frac{1}{10}-\frac{1}{15}= \frac{-3-2}{30}=-\frac{5}{30}=-\frac{1}{6}$
$\therefore \text{f}=-6\text{cm}$
$\therefore $ The focal length of the concave mirror is 6cm.


$\text{Refractuive index of the medium}=\frac{\text{Speed of light in air}}{\text{Speed of light in medium }}$
$1.2=\frac{300000}{\text{speed of light medium}}$
${\text{Speed of light in medium}}=250000\text{km/ s}$
$\text{f}=\frac{\text{R}}{2}$
R= 25cm (Given) f = ? We know that$\text{f}=\frac{\text{R}}{2}$
$=\frac{25}{2}$
$\text{f} = 12.5\text{cm}$
$\frac{1}{\text{v}}+ \frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\Rightarrow\frac{1}{\text{v}}+ \frac{1}{(-20)}=\frac{1}{\text{(-20)}}$
$\Rightarrow \frac{1}{\text{v}}=0$
$\therefore \text{v}=\text{infinity}$
$\frac{1}{\text{v}}-\frac{1}{\text{u}}=\frac{1}{\text{f}}$
$\frac{1}{\text{v}}-\frac{1}{-10}=\frac{1}{10}$
$\frac{1}{\text{v}}=0$
$\text{v}=\frac{1}{0}=\infty$
At infinity.
Principal focus of a convex mirror: The principal focus of a convex mirror is a point on its principal axis from which a beam of light rays, initially parallel to the axis, appears to diverge after being reflected from the convex mirror.
Focal length of a concave mirror: The focal length of a convex mirror is the distance from the pole (P) to its principal focus (F).

$\text{Refractive index of water}=\frac{\text{Speed of light in vacuum}}{\text{Speed of light in water}}$
$\text{Refractive index of water}=\frac{3\times10^8}{2.25\times10^8}=1.33$
$\text{n}_\text{wa}=\frac{\text{v}_\text{a}}{\text{v}_\text{w}}$
$\frac{4}{3}=\frac{3\times10^8}{\text{v}_\text{w}}$
On calculating we get velocity of light in water -2.25 x 108m/s$\text{Refractive index of glass}=\frac{\text{Speed of light in air}}{\text{Speed of light in glass}}$
$1.5=\frac{3\times10^8}{\text{Speed of light in glass}}$
$\text{Speed of light in glass}=2\times10^8\text{m/ s}$
$\text{P}=\frac{1}{\text{f}}$
$\text{f}=\frac{1}{\text{P}}=\frac{1}{0.5}=2\text{m}$
