Define the term power of a lens.

$(a)$ Water has a refractive index of $1.33$ and alcohol has a refractive index of $1.36$. Which of the two media is optically denser? Give a reason for your answer. Draw a ray diagram to show the path of a ray of light passing obliquely from water to alcohol.
$(b)$ The absolute refractive index of diamond is $2.42$ and the absolute refractive index of glass is $1.50$. Find the refractive index of diamond with respect to glass.

One half of a convex lens of focal length $10\, cm$ is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of $30\, cm$ from the lens? Draw a ray diagram to justify your answer.
$A$ $4\, cm$ tall object is placed perpendicular to the principal axis of a convex lens of focal length $20\, cm$. The distance of the object from the lens is $15\, cm$. Find the nature,position and size of the image.

The figure below shows a point source of light $S$,a convex lens $L$,and a plane mirror $M$. The three are placed such that rays of light from $S$ return to it after reflection from $M$. $(i)$ What is the distance $OS$ called? $(ii)$ To which point (left of $S$,on $S$,or right of $S$) will the rays return if $M$ is moved to the left and brought in contact with $L$?

The nature,size,and position of the image of an object produced by a lens or mirror are as shown below. Identify the lens/mirror $(X)$ used in each case and draw the corresponding complete ray diagram.

When is the magnitude of the power of a lens equal to its focal length?