Q1: A
convex mirror has its radius of curvature 20 cm. Find the position of the image of an object placed at a distance of
12 cm from the mirror.
[Ans 
,virtual]
Q2: An
object of length 2.5 cm is placed at a
distance of 1.5 f from a
concave mirror where f is the magnitude of the focal length of the mirror. The
length of the object is perpendicular to the principal axis. Find the length of
the image. Is the image erect or inverted ? [Ans
5cm, Inverted]
Q3: An
object of length 2.0 cm is placed
perpendicular to the principal axis of a convex lens of focal length 12
cm. Find the size of the image if the
object is at a distance of 8.0 cm from
the lens.
[Ans
6.0cm, Erect]
Q4: An
object is placed on the principal axis of a concave mirror of focal length 10 cm at a distance of 8.0 cm from the pole. Find the position and the
nature of the image. [Ans
40cm, Virtual]
Q5: A rod of length 10 cm lies along the principal axis of a concave
mirror of focal length 10 cm in
such a way that the end closer to the pole is 20 cm away from it. Find the length of the image.
[Ans
5cm]
Q6:
At what distance from a convex mirror of focal length 2.5
m should a boy stand so that his image
has a height equal to half the original height ? The principal axis is perpendicular to the height.
[Ans
2.5cm]
Q7:
A 2.0 cm high object is
placed on the principal axis of a concave mirror at a distance of 12 cm from the pole. If the image is inverted,
real and 5.0 cm high, find the location
of the image and the focal length of the mirror. [Ans 30cm(object
side), 8.6cm]
Q8**:
A slide projector produces 500 times enlarged image of a slide on a screen 10 m away. Assume that the projector consists of
a single convex lens used for magnification. If the screen is moved 2.0
m closer, by what distance should the
slide be moved towards or away from the lens so that the image remains focussed
on the screen ?
[Ans 
cm. away from
lens]
Q9: A
concave mirror having a radius of curvature 40 cm is placed in front of an
illuminated point source at a distance of 30 cm from it. Find the location of the
image.
[Ans
60 cm from the mirror on the side of object]
Q10: A concave mirror
forms an image of 20 cm high object on a screen placed 5.0 m away from the
mirror. The height of the image is 50 cm. Find the focal length of the mirror
and the distance between the mirror and the object. [Ans
1.43 m, 2.0 m]
Q11: A concave mirror
has a focal length of 20 cm. Find the position or positions of an object for
which the image size is double of the object-size. [Ans 10 cm or 30 cm from
the mirror]
Q12: A 1 cm object is
placed perpendicular to the principal axis of a convex mirror of focal length
7.5 cm. Find its distance from the mirror if the image formed is 0.6 cm in
size. [Ans
5 cm]
Q13: A 3 cm tall object
is placed at a distance of 7.5 cm from a convex mirror of focal length 6 cm.
Find the location, size and nature of the image.
[Ans
cm from the mirror on the side opposite to the object,
1.33 cm, virtual and erect]
Q14: A man uses a
concave mirror for shaving. He keeps his face at a distance of 25 cm from the
mirror and gets an image which is 1.4 times enlarged. Find the focal length of
the mirror.
[Ans 87.5 cm]
Q15: An object
is placed at (i) 10 cm, (ii) 5 cm in front of a concave mirror of radius of
curvature 15 cm. Find the position, nature, and magnification of the image in
each case.
[Ans.
i. -30 cm, m=-3, magnified, real and inverted. ii 15 cm, m=3, magnified,
virtual and erect.]
Q16**: Suppose while
sitting in a parked car, you notice a jogger approaching towards you in the
side view mirror of R = 2 m. If the jogger is running at a speed of 5
, how fast the image of the jogger appear to move when
the jogger is (a) 39 m, (b) 29 m, (c) 19 m, and (d) 9 m away.
[Ans. 
m/s, 
m/s and 
m/s]
Q17: A small candle, 2.5 cm in size is
placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. 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?
[Ans. v = –54 cm. The image is
real, inverted and magnified. The size of the image is 5.0 cm. As u
f, 
; for u < f, image is virtual.]
Q18: A 4.5 cm needle is placed 12 cm
away from a convex mirror of focal length 15 cm. Give the location of the image
and the magnification. Describe what happens as the needle is moved farther
from the mirror.
[Ans. v = 6.7 cm. Magnification
= 5/9, i.e., the size of the image is 2.5 cm. As 
; v f (but
never beyond) while m 0.]
Q19: Double-convex lenses are to be
manufactured from a glass of refractive index 1.55, with both faces of the same
radius of curvature. What is the radius of curvature required if the focal
length is to be 20cm? [Ans.
1.33; 1.7 cm]
Q20: Double-convex lenses are to be
manufactured from a glass of refractive index 1.55, with both faces of the same
radius of curvature. What is the radius of curvature required if the focal
length is to be 20cm? [R
= 22 cm]
Q21: A beam of light converges at a
point P. Now a lens is placed in the path of the convergent beam 12cm from P.
At what point does the beam converge if the lens is (a) a convex lens of focal
length 20cm,
and (b) a concave lens of focal length
16cm?
[Ans. Here the object is virtual and
the image is real. u = +12 cm (object on right; virtual)
(a) f = +20 cm. Image is real
and at 7.5 cm from the lens on its right side.
(b) f = –16 cm. Image is real
and at 48 cm from the lens on its right side.]
Q22: An object of size 3.0cm is placed
14cm in front of a concave lens of focal length 21cm. Describe the image
produced by the lens. What happens if the object is moved further away from the
lens?
[Ans. v = 8.4 cm, image is
erect and virtual. It is diminished to a size 1.8 cm. As u
, v f (but never beyond f while m 0). Note
that when the object is placed at the focus of the concave lens (21 cm), the
image is located at 10.5 cm (not at infinity as one might wrongly think).]
Q23: What is the focal length of a
convex lens of focal length 30cm in contact with a concave lens of focal length
20cm? Is the system a converging or a diverging lens? Ignore thickness of the
lenses.
[Ans.
A diverging lens of focal length 60 cm]
Q24: Use the mirror equation to deduce
that:
(a) an object placed between f and
2f of a concave mirror produces a real image beyond 2f.
(b) a convex mirror always produces a
virtual image independent of the location of the object.
(c) the virtual image produced by a
convex mirror is always diminished in size and is located between the focus and
the pole.
(d) 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.]
[Ans. Apply mirror equation and the
condition:
(a) f < 0 (concave mirror); u
< 0 (object on left)
(b) f > 0; u < 0
(c) f > 0 (convex mirror)
and u < 0
(d) f < 0 (concave mirror); f
< u < 0
to deduce the desired result.]
Q25: The image of a small electric
bulb fixed on the wall of a room is to be obtained on the opposite wall 3m away
by means of a large convex lens. What is the maximum possible focal length of
the lens required for the purpose? [Ans. For fixed distance s between
object and screen, the lens equation does not give a real solution for u or
v if f is greater than s/4. Therefore, fmax = 0.75
m.]
Q26: A screen is placed 90cm from an
object. The image of the object on the screen is formed by a convex lens at two
different locations separated by 20cm. Determine the focal length of the lens.
[Ans. 21.4 cm]
Q27: An object approaches a convergent
lens from the left of the lens with a uniform speed 5 m/s and stops at the
focus. The image
(a) moves away from the lens with an
uniform speed 5 m/s.
(b) moves away from the lens with an
uniform accleration.
(c) moves away from the lens with a
non-uniform acceleration.
(d) moves towards the lens with a
non-uniform acceleration.
[(c)]
Q28: The radius of curvature of the
curved surface of a plano-convex lens is 20 cm. If the refractive index of the
material of the lens be 1.5, it will
(a) act as a convex lens only for the
objects that lie on its curved side.
(b) act as a concave lens for the
objects that lie on its curved side.
(c) act as a convex lens irrespective
of the side on which the object lies.
(d) act as a concave lens irrespective
of side on which the object lies.
[(c)]
[(b)]
(a) 1
(b) 2
(c) 3
(d) 4
[(b)]
Q30: A car is moving with at a
constant speed of 60 km h–1 on a straight road. Looking at the rear view
mirror, the driver finds that the car following him is at a distance of 100 m
and is approaching with a speed of 5 km h –1. In order to keep track of the car
in the rear, the driver begins to glance alternatively at the rear and side
mirror of his car after every 2 s till the other car overtakes. If the two cars
were maintaining their speeds, which of the following statement (s) is/are
correct?
(a) The speed of the car in the rear
is 65 km h–1.
(b) In the side mirror the car in the
rear would appear to approach with a speed of 5 km h–1 to the driver
of the leading car.
(c) In the rear view mirror the speed
of the approaching car would appear to decrease as the distance between the
cars decreases.
(d) In the side mirror, the speed of
the approaching car would appear to increase as the distance between the cars
decreases.
[(d)]
