Question

1.The distance between the object and its inverted image formed by a concave mirror is
25cm. If the magnification produced by the mirror is -2, use mirror formula to
determine the object distance, image distance and focal length of the mirror. Draw a ray
diagram to illustrate image formation in this case and also mark the distances on it.
2. The image of an object formed by mirror is real inverted and is of magnification -1. If
the image is at a distance of 40cm from the mirror, where is the object placed? Where
would the image be if the object is moved 20cm towards the mirror? State reason and
also draw ray diagram for the new position of the object to justify your answer.
3. A concave mirror produces three times magnified image real image of an object placed
at 10cm in front of it. Where is the image located?
4. Radius of curvature used in an automobile is 2m. A truck is coming behind it at a
constant distance of 3.5m. Calculate the position and size of the image relative to the
truck. Find the nature of the image.
5. A shaving mirror having radius of curvature 64cm is held at a distance of 16cm from
the user. Calculate position of image and magnification.
6. A convex mirror of r = 4m is used as a rearview mirror in a car. If a truck is located at a
distance of 6m from the mirror, find position, nature and size of the image.
7. A 2cm high object is kept 20cm from a concave mirror. If a real image is formed at
50cm from the mirror, find the focal length of the mirror and size of image.
8. An object of size 7cm is placed at 27cm from a concave mirror of f=18cm. At what
distance should a screen be placed, so that a sharp focused image can be obtained?
9. The magnification produced by a concave mirror is -0.5 when an object is placed at a
distance of 40cm from it. Where should the object be placed to get a magnification of -
0.2?
10. An object is placed at a distance of 10cm from a convex mirror of focal length 15cm.
Find position and nature of image.
11. A convex mirror with radius of curvature 30cm has an object 20cm in front of it. If size
of the object is 5cm, find position, nature and size of image.
12. An object is placed at a distance of 25cm from a mirror. The mirror produces an image
that is 20 cm (i) behind the mirror; and (ii) in front of the mirror.
a. For each case, find focal length of the mirror and nature of mirror

Answer 1

Answer:

★ Using the Real-Is-Positive convention makes sense here, since everything is real, and therefore positive. (Besides, I never learned the other convention or even encountered it)

1/f = 1/u + 1/v

u = 30 and v = 10

1/f = 1/10 + 1/30 = 3/30 + 1/30 = 4/30 = 1/7.5

Invert: f = +7.5

★ magnification(m) = -3 (as image is real)

object distance(u) = -10cm

image distance (v)=?

we know that m= -v/u

-3 = -v /-10

-3 = v/10

v =-3 * 10

v = - 30 cm