Advertisements
Advertisements
Question
An object is placed vertically at a distance of 20 cm from a convex lens. If the height of the object is 5 cm and the focal length of the lens is 10 cm, what will be the position, size and nature of the image? How much bigger as compared to the object?
Advertisements
Solution
Given: Height of the object (h1) = 5 cm,
focal length (f) = 10 cm,
distance of the object (u) = –20 cm
To find: Image distance (v), height of the image (h2), magnification (M)
Formulae:
- `1/"v" - 1/"u" = 1/"f"`
- Magnification (M) = `"h"_2/"h"_1 = "v"/"u"`
Calculation: From formula (i),
`1/"v" = 1/"u" + 1/"f"`
∴ `1/"v" = 1/(-20) + 1/10`
∴ `1/"v" = (- 1 + 2)/20`
∴ `1/"v" = 1/20`
∴ v = 20 cm
From formula (ii),
`"h"_2 = "v"/"u" xx "h"_1`
∴ `"h"_2 = 20/(- 20) xx 5`
∴ `"h"_2 = (- 1) xx 5`
∴ `"h"_2` = - 5 cm
∴ M = `"v"/"u" = 20/(-20)` = - 1
The negative sign of the height of the image and the magnification shows that the image is inverted and real. It is below the principal axis and is of the same size as the object.
APPEARS IN
RELATED QUESTIONS
A student has obtained a point image of a distant object using the given convex lens. To find the focal length of the lens he should measure the distance between the :
(A) lens and the object only
(B) lens and the screen only
(C) object and the image only
(D) lens and the object and also between the object and the image
The image of a candle flame placed at a distance of 30 cm from a spherical lens is formed on a screen placed on the other side of the lens at a distance of 60 cm from the optical centre of the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 3 cm, find the height of its image.
At what distance from a concave lens of focal length 20 cm, should a 6 cm tall object be placed so that it forms an image at 15 cm from the lens ? Also determine the size of the image formed.
A spherical mirror produces an image of magnification -1 on a screen placed at a distance of 50 cm from the mirror.
(a) Write the type of mirror.
(b) Find the distance of the image from the object.
(c) What is the focal length of the mirror?
(d) Draw the ray diagram to show the image formation in this case.
A student has obtained an image of a distant object on a screen to determine the focal length F1 of the given lens. His teacher, after checking the image, gave him another lens of focal length F2 and asked him to focus the same object on the same screen. The student found that to obtain a sharp image, he has to move the lens away from the screen. From this finding, we may conclude that both the lenses given to the student were :
(A) Concave and F1 < F2
(B) Convex and F1 < F2
(C) Convex and F1 > F2
(D) Concave and F1 > F2
An object is held 20 cm away from a converging lens of focal length 10 cm. Find the position of the image formed.
The image seen in a plane mirror cannot be formed on a screen. What name is given to this type of image?
What is the difference between a real image and a virtual image? Give one example of each type of image
When an object is placed at a distance of 50 cm from a concave spherical mirror, the magnification produced is, `-1/2`. Where should the object be placed to get a magnification of, `-1/5`?
An object is placed (a) 20 cm, (b) 4 cm, in front of a concave mirror of focal length 12 cm. Find the nature and position of the image formed in each case.
Linear magnification produced by a concave mirror may be:
(a) less than 1 or equal to 1
(b) more than 1 or equal than 1
(c) less than 1, more than 1 or equal to 1
(d) less than 1 or more than 1
In order to obtain a magnification of −2 (minus 2) with a concave mirror, the object should be placed:
(a) between pole and focus
(b) between focus and centre of curvature
(c) at the centre of curvature
(d) beyond the centre of curvature
A concave mirror produces magnification of +4. The object is placed:
(a) at the focus
(b) between focus and centre of curvature
(c) between focus and pole
(d) between the centre of curvature
If a magnification of, −1 (minus one) is to be obtained by using a converging mirror, then the object has to be placed:
(a) between pole and focus
(b) at the centre of curvature
(c) beyond the centre of curvature
(d) at infinity
Draw a diagram to show how a converging lens held close to the eye acts as a magnifying glass. Why is it usual to choose a lens of short focal length for this purpose rather than one of long focal length?
The lens A produces a magnification of, − 0.6 whereas lens B produces a magnification of + 0.6.
What is the nature of lens B?
Draw a ray diagram to show how a converging lens is used as a magnifying glass to observe a small object. Mark on your diagram the foci of the lens and the position of the eye.
A student wants to project the image of a candle flame on a screen 80 cm in front of a mirror by keeping the candle flame at a distance of 20 cm from its pole.
- Which type of mirror should the student use?
- Find the magnification of the image produced.
- Find the distance between the object and its image.
- Draw a ray diagram to show the image formation in this case and mark the distance between the object and its image.
An object of height 6 cm is placed perpendicular to the principal axis of a concave lens of focal length 5 cm. Use lens formula to determine the position, size and nature of the image if the distance of the object from the lens is 10 cm.
The image of a candle flame placed at a distance 30 cm from a spherical lens is formed on a screen placed at a distance of 60 cm from the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 2.4 cm, find the height of its image.
The image of a candle flame placed at a distance 36 cm from a spherical lens is formed on a screen placed at a distance of 72 cm from the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 2.5 cm, find the height of its image.
At which position will you keep an object in front of a convex lens so as to get a real image of the same size as the object? Draw a figure.
Give a scientific reason.
Simple microscope is used for watch repairs.
Solve the following example.
An object kept 60 cm from a lens gives a virtual image 20 cm in front of the lens. What is the focal length of the lens? Is it a converging lens or diverging lens?
At which position will you keep an object in front of convex lens to get a real image smaller than the object? Draw a figure.
A lens forms the image of an object placed at a distance 15 cm from it, at a distance 60 cm in front of it. Find the magnification.
Magnification of a convex lens is ______.
A lens of focal length 5 cm is being used by Debashree in the laboratory as a magnifying glass. Her least distance of distinct vision is 25 cm.
- What is the magnification obtained by using the glass?
- She keeps a book at a distance 10 cm from her eyes and tries to read. She is unable to read. What is the reason for this?
Ravi kept a book at a distance of 10 cm from the eyes of his friend Hari. Hari is not able to read anything written in the book. Give reasons for this?
The magnification produced when an object is placed at a distance of 20 cm from a spherical mirror is +1/2. Where should the object be placed to reduce the magnification to +1/3.
Write an expression for magnification for a lens, explaining the meaning of the symbols used.
What information about the nature of image is erect or inverted, do you get from the sign of magnification + or -?
