The radius of curvature of a spherical mirror is $20\, cm$. What is its focal length (in $cm$)?

Find out,from the table,the medium having the highest optical density. Also,find the medium with the lowest optical density.

Material medium	Refractive index
Air	$1.0003$
Ice	$1.31$
Water	$1.33$
Alcohol	$1.36$
Kerosene	$1.44$
Fused quartz	$1.46$
Turpentine oil	$1.47$
Benzene	$1.50$
Crown glass	$1.52$
Canada Balsam	$1.53$
Rock salt	$1.54$
Carbon disulphide	$1.63$
Dense flint glass	$1.65$
Ruby	$1.71$
Sapphire	$1.77$
Diamond	$2.42$

$A$ convex lens forms a real and inverted image of a needle at a distance of $50\, cm$ from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also,find the power of the lens.

Light enters from air to glass having refractive index $1.50$. What is the speed of light in the glass? The speed of light in vacuum is $3 \times 10^8 \, m \, s^{-1}$.

You are given kerosene,turpentine,and water. In which of these does the light travel fastest? Use the information given in the table below.

Material medium	Refractive index
Water	$1.33$
Kerosene	$1.44$
Turpentine oil	$1.47$

Define the principal focus of a concave mirror.