Advertisements
Advertisements
प्रश्न
A convex mirror has a focal length of 18 cm. The image of an object kept in front of the mirror is half the height of the object. What is the distance of the object from the mirror?
Advertisements
उत्तर
Given:
Focal length (f) = 18 cm
Magnifiction (M) = `("Height of the image" ("h"_2))/("Height of the object" ("h"_1))`
= `1/2`
Find: Object distance (u)
Formula:
- M = `("h"_2)/("h"_1) = -"v"/"u"`
- `1/"f" = 1/"v" + 1/"u"`
Calculations:
According to formula (i),
`1/2 = -"v"/"u"`
∴ v = `-"u"/2`
According to formula (ii),
`1/"f" = 1/"v" + 1/"u" = ("u" + "v")/("uv")`
∴ f = `("uv")/ ("u" + "v")`
Now, v = `-"u"/2`
∴ f = `("u"((-"u")/2))/("u" + ((-"u")/2))`
∴ `18 = ((-"u"^2)/2)/((2"u" - "u")/2) = (-"u"^2)/"u"`
∴ u = −18 cm
A negative sign indicates that the object is placed to the left of the mirror.
Hence, the distance of the object from the mirror is 18 cm.
APPEARS IN
संबंधित प्रश्न
The height of the image formed by an object of height 10 cm placed in front of a plane mirror is __________.
(a) 5 cm
(b) 10 cm
(c) 15 cm
(d) 20 cm
For which positions of the object does a concave mirror produce an inverted, magnified an real image?
What sign (+ve or −ve) has been given to the following on the basis of Cartesian Sigh Convention?
Height of a virtual image.
Describe the New Cartesian Sigh Convention used in optics. Draw a labelled diagram to illustrate this sign convention.
An object 20 cm from a spherical mirror gives rise to virtual image 15 cm behind the mirror. Determine the magnification of the image and the type of mirror used.
Write down the magnification formula for a lens in terms of object distance and image distance. How does this magnification formula for a lens differ from the corresponding formula for a mirror?
An object is placed at a distance of 100 cm from a converging lens of focal length 40 cm.
(i) What is the nature of image?
(ii) What is the position of image?
An erect image 2.0 cm high is formed 12 cm from a lens, the object being 0.5 cm high. Find the focal length of the lens.
A lens of focal length 20 cm is used to produce a ten times magnified image of a film slide on a screen. How far must the slide be placed from the lens?
A convex lens produces a magnification of + 5. The object is placed:
(a) at focus
(b) between f and 2f
(c) at less than f
(d) beyond 2f
If a magnification of, –1 (minus 1) is obtained by using a converging lens, then the object has to be placed:
(a) within f
(b) at 2f
(c) beyond 2f
(d) at infinity
An object is 0.09 m from a magnifying lens and the image is formed 36 cm from the lens. The magnification produced is:
(a) 0.4
(b) 1.4
(c) 4.0
(d) 4.5
To obtain a magnification of, –2 with a convex lens of focal length 10 cm, the object should be placed:
(a) between 5 cm and 10 cm
(b) between 10 cm and 20 cm
(c) at 20 cm
(d) beyond 20 cm
An image formed on a screen is three times the size of the object. The object and screen are 80 cm apart when the image is sharply focussed.
Calculate focal length of the lens.
Magnification produced by a rear view mirror fitted in vehicles ______.
For a plane mirror, magnification m = ______.
Magnification for the convex mirror is ______.
What do you mean by linear magnification?
