Curved Mirror

If the equation of mirror is given by $\mathrm{y}=2/\mathrm{\pi } \mathrm{sin\pi x} \left(\mathrm{y}>0,0\le \mathrm{x}\le 1\right)$  then find the point on which horizontal ray should be incident so that the reflected ray become perpendicular to the incident ray

A ray of light is incident oa a concave mirror. It is to the principal axis and its height from principal axis is equal to the focal length of the mirror. The ratio of the distance of point $\mathrm{B}$ to the distance of the focus from the centre of curvature is ($\mathrm{AB}$ is reflected ray)

A converging lens of focal length $f_1$ is placed in front of and coaxial with a convex mirror of focal length $f_2$. Their separation is $d$. A parallel beam of light incident of the lens returns as a parallel beam from the arrangement-

A thief is running away in a car with velocity of $20 {\mathrm{ms}}^{-1}$. A police jeep is following him, which is sighted by thief in his rear view mirror which is a convex  mirror of focal length $10 \mathrm{m}$. He observes that the image of jeep is moving towards him with a velocity of of $1 \mathrm{cm} {\mathrm{s}}^{-1}$. If the magnification of the mirror for the jeep at that time is $\frac{1}{10}$. Find (a) actual speed of jeep (b) rate at which magnification is changing. Assume that police jeep is on axis of the mirror.

A fly $F$ is sitting on a glass slab, $A$, $45 \mathrm{cm}$ thick of refractive index $\frac{3}{2}$. The slab covers the top of a container $B$ containing water (Refractive index $\frac{4}{3}$) upto a height of $20 \mathrm{cm}$. The bottom of container is closed by a concave mirror $C$ of radius of curvature $40 \mathrm{cm}$. Find the distance (in $\mathrm{cm}$) of final image from $F$ formed by all refractions and reflection assuming paraxial rays.

A balloon is rising up along the axis of a concave mirror of radius of curvature $20 \mathrm{m}$. A ball is dropped from the balloon at a height $15 \mathrm{m}$ from the mirror when the balloon has velocity $20 \mathrm{m} {\mathrm{s}}^{-1}$. Find the speed (in $\mathrm{m} {\mathrm{s}}^{-1}$) of the image of the ball formed by a concave mirror after $4$ seconds? [Take : $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

Two concave mirrors each of radius of curvature $40 \mathrm{cm}$ are placed such that their principal axes are parallel to each other & at a distance of $1 \mathrm{cm}$ to each other. Both the mirrors are at a distance of $100 \mathrm{cm}$ to each other. Consider first reflection at $M_1$ and then at $M_2$, the final coordinates of the image thus formed are $\left(x,-y\right)$, then find $\frac{x}{y}$. Take location of object as the origin.

When a pin is moved along the principal axis of a small concave mirror, the image position coincides with the object at a point $0.5 \mathrm{m}$ from the mirror, refer to figure. If the mirror is placed at depth of $0.2 \mathrm{m}$ in a transparent liquid, the same phenomenon occurs when the pin is placed $0.4 \mathrm{m}$ form the mirror. The refractive index of the liquid is:  

A convex mirror of focal length $\text{'}f\text{'}$ is placed at the origin with its reflecting surface towards the negative x-axis. Choose the correct graphs between $\text{'}v\text{'}$ and $\text{'}u\text{'}$ for $u<0$. 

Radius of curvature of each mirror is $\mathrm{R}$. $\mathrm{O}$ is object. Consider first reflection from concave mirror. Consider only first three reflection. The distance of final image from convex mirror is 

A concave mirror of focal length $20\mathrm{cm}$ is cut into two parts from the middle and the two parts are moved perpendicularly by a distance $1\mathrm{mm}$ from the previous principal axis $\mathrm{AB}$. The distance between the images formed by the two parts is:

An infinitely long rod lies along the axis of a concave mirror of focal length $f$. The near end of the rod is at a distance $u>f$ from the mirror. Its image will have a length

A short linear object of length $b$ lies along the axis of a concave mirror of focal length $f,$at a distance $u$ from the mirror. The size of the image is approximately

The distance of an object from a spherical mirror is equal to the focal length of the mirror. Then the image :