Reflection of Light by Spherical Mirrors

When using a concave mirror, the magnification is found to be $4$ times as much when the object is $25 \mathrm{cm}$ from the mirror as it is with the object at $40 \mathrm{cm}$ from the mirror, the image being real in each case. What Is the focal length of the mirror?

Find two positions of an object, placed In front of a concave mirror of focal length $15 \mathrm{cm}$, so that the Image formed is $3$ times the size of the object.

Using a neat labelled diagram derive the mirror equation. Define linear magnification.

An object of $5 \mathrm{cm}$ height is placed at a distance of $15 \mathrm{cm}$ from a concave mirror of radius of curvature $20 \mathrm{cm}$. Find the size of the image.

What is the cartesian sign convention? Applying this convention and using a neat diagram, derive an expression for finding the image distance using the mirror equation.

A mobile phone lies along the principal axis of a concave mirror longitudinally. Explain why the magnification is not uniform.

Explain the Cartesian sign convention for mirrors. 
 

Define focal length of a concave mirror. Prove that the radius of curvature of a concave mirror is double its focal length. 
 

What are the laws of reflection through curved mirrors? 

A concave mirror produces an image of a long vertical pin, placed $40 \mathrm{cm}$ from the mirror, at the position of the object. Find the focal length of the mirror (in $\mathrm{cm}$). 
 

A tank is filled with water to a height of $12.5 \mathrm{c}\mathrm{m}$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \mathrm{c}\mathrm{m}$. What is the refractive index of water? If water is replaced by a liquid of refractive index $1.63$ up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

Use the mirror equation to deduce that: an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image. [Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

Use the mirror equation to deduce that:
the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.
[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

Use the mirror equation to deduce that:
A convex mirror always produces a virtual image independent of the location of the object.
[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

Answer the following questions:
You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.

Use the mirror equation to deduce that:
an object placed between $f$ and $2f$ of a concave mirror produces a real image beyond $2f$.
[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

A $4.5 \mathrm{c}\mathrm{m}$ needle is placed $12 \mathrm{c}\mathrm{m}$ away from a convex mirror of focal length $15 \mathrm{c}\mathrm{m}$. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

A small candle, $2.5 \mathrm{c}\mathrm{m}$ in size is placed at $27 \mathrm{c}\mathrm{m}$ in front of a concave mirror of radius of curvature $36 \mathrm{c}\mathrm{m}$. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?