Advertisements
Advertisements
Question
Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to 1/3rd of its size. At what distance the object has been placed from the mirror? What is the nature of the image and the mirror?
Advertisements
Solution
Case I: (In case of convex mirror)
Magnification, `"m" = 1/3` (convex mirror)
Focal length (f) = 20 cm
Size of image `("h"_"i") = 1/3 xx "h"_"o"` (Size of object)
Using the magnification formula,
`"m" = "h"_"i"/"h"_"o" = (-upsilon)/"u"`
Substituting the values in the above equation,
`("h"_"o"/3)/"h"_"o" = (-upsilon)/"u"`
`1/3 = (-upsilon)/"u"`
`upsilon = (-"u")/3`
Using the mirror formula,
`1/upsilon + 1/"u" = 1/"f"`
`(-3)/"u" + 1/"u" = 1/20`
`(-2)/"u" = 1/20`
u = -40 cm
Negative sign shows that the object is in front of the mirror.
Substituting the above value in obtained image distance and object distance relation,
`upsilon = -u/3 = - ((-40))/3 = 40/3` cm
Thus, the image formed is virtual, erect and diminished. The object is at a distance of 40 cm from the mirror.
Case II: In case of concave mirror
Magnification, `"m" = -1/3` (concave mirror)
Focal length (f) = -20 cm
Using the magnification formula,
`"m" = "h"_"i"/"h"_"o" = (-upsilon)/"u"`
Substituting the values in the above equation,
`(-1)/3 = (-upsilon)/"u"`
`1/3 = upsilon/"u"`
`upsilon = "u"/3`
Using the mirror formula,
`1/upsilon + 1/"u" = 1/"f"`
`3/"u" + 1/"u" = 1/(-20)`
`4/"u" = 1/(-20)`
u = -80 cm
`upsilon = "u"/3 = -80/3` cm
Thus, the image will be real and inverted. The object is at a distance of 80 cm from the mirror.
APPEARS IN
RELATED QUESTIONS
Define the following term in the context of spherical mirrors:- Pole
We can obtain a real, enlarged and inverted image by a concave mirror.
What type of image is formed:
in a plane mirror?
The shiny outer surface of a hollow sphere of aluminium of radius 50 cm is to be used as a mirror:
State whether this spherical mirror will diverge or converge light rays.
A ray of light travels from a denser medium to a rarer medium. How will it bend?
What do you mean by the term dispersion?
State the direction of incident ray which after reflection from a spherical mirror gets reflected along its own path. Give a reason.
What is a spherical mirror?
Draw a ray diagram to show the formation of image by a concave mirror for the object beyond its centre of curvature. State three characteristics of the image.
(a) When a concave mirror is used as a shaving mirror, where is the person's face in relation to the focus of mirror?
(b) State three characteristics of the image seen in part (a).
The erect image formed by a concave mirror is of size double the size of object. How are u and v related?
An object of length 4 cm is placed in front of a concave mirror at distance 30 cm. The focal length of mirror is 15 cm.
- Where will the image form?
- What will be the length of image?
When an object of height 1 cm is kept at a distance 4 cm from a concave mirror, its erect image of height 1.5 cm is formed at a distance 6 cm behind the mirror. Find the focal length of mirror, by drawing.
A point light source is kept in front of a convex mirror at a distance of 40 cm. The focal length of the mirror is 40 cm. Find the position of image.
Define the following term:
spherical mirror
Define the term Aperture.
The diagram below shows the parallel rays incident on a convex mirror. C is the centre of the curvature of the mirror. By drawing the paths of the reflected rays, label the focus F and hence find the focal length of the mirror.
If the focal length of a spherical mirror is 10 cm, what is the value of its radius of curvature?
