**Numerical Problems Based on Mirror Formula for Class 12 Physics**

**Q.1.** A 5 cm long needle is placed 10 cm from a convex mirror of focal length 40 cm. Find the position, nature and size of the image of the needle. What happens to the size of image when the needle is moved farther away from the mirror?

**Q.2.** An object is placed (i) 10 an, (ii) 5 cm in front of a concave mirror of radius of curvature 15 an Find the position, nature and magnification of the image in each case.

**Q.3.** A concave mirror of focal length 10 cm is placed at a distance of 35 cm from a wall. How far from the wall should an object be placed to get its image on the wall?

**Q.4.** A thin rod of length f/3 is placed along the optic axis of a concave mirror of focal length ‘f’ such that its image which is real and elongated, just touches the rod. What will be the magnification?

**Q.5. **An object is kept in front of a concave mirror of focal length 15 cm The image formed is three times the size of the object. Calculate the two possible distances of the object from the mirror.

**Q.6.** An object is placed at a distance of 40 cm on the principal axis of a concave mirror of radius of curvature 30 cm. By how much does the image move if the object is shifted towards the mirror through 15 cm?

**Q.7.** When the distance of an object from a concave mirror is decreased from 15 cm to 9 cm the image gets magnified 3 times than that in first case. Calculate the focal length of the mirror.

**Q.8.** Calculate the distance of an object of height h from a concave mirror of radius of curvature 20 cm, so as to obtain a real image of magnification 2. Find the location of image also.

**Q.9.** Two objects A and B when placed one after another in front of a concave mirror of focal length 10 cm, form images of same size. Size of object A is 4 times that of B. If object A is placed at a distance of 50 cm from the mirror, what should be the distance of B from the mirror?

**Q.10. **An object is placed at a distance of 36 cm from a convex mirror. A plane mirror is placed in between so that the two virtual images so formed coincide. If the plane mirror is at a distance of2i cm from the object, find the radius of curvature of the convex mirror.

**Q.11. **A square wire of side 3.0 cm is placed 25 cm away from a concave mirror of focal length 10 cm What is the area enclosed by the image of the wire? (The centre of the wire is on the axis of the mirror, with its two sides normal to the axis).

**Q.12.** If you sit in a parked car, you glance in the rear-view mirror R= 2 m and notice a jogger approaching. If the jogger is running at a speed of 5 ms^{-1}, how fast is the image of the jogger moving when the jogger is (a) 39 m (b) 29 m (c) 19 m (d) 9 m away?