Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
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.
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
A student was asked by his teacher to find the image distance for various object distance in case of a given convex lens. He performed the experiment with all precautions and noted down his observations in the following table:
| S. No. |
Object distance (cm) |
Image distance (cm) |
| 1 | 60 | 15 |
| 2 | 48 | 16 |
| 3 | 36 | 21 |
| 4 | 24 | 24 |
| 5 | 18 | 36 |
| 6 | 16 | 48 |
After checking the observations table the teacher pointed out that there is a mistake in recording the image distance in one of the observations. Find the serial number of the observations having faulty image distance.
(A) 2
(B) 3
(C) 5
(D) 6
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
Magnification produced by a convex mirror is always:
(a) more than 1
(b) less than 1
(c) equal to 1
(d) more or less 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
In order to obtain a magnification of, −1.5 with a concave mirror of focal length 16 cm, the object will have to be placed at a distance
(a) between 6 cm and 16 cm
(b) between 32 cm and 16 cm
(c) between 48 cm and 32 cm
(d) beyond 64 cm
Linear magnification (m) produced by a rear view mirror fitted in vehicles:
(a) is equal to one
(b) is less than one
(c) is more than one
(d) can be more less than one depending on the position of object
Explain what is meant by a virtual, magnified image.
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?
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.
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?
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.
An object is placed at a distance of 20 cm in front of a concave lens of focal length 20 cm.
- Find the position of the image, and
- the magnification of the image.
Find the position and magnification of the image of an object placed at distance of 8.0 cm in front of a convex lens of focal length 10.0 cm. Is the image erect or inverted?
The lens of the eye is flattened when looking at nearby objects.
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 focal length of a concave lens is 20 cm. At what distance from the lens should a 5 cm tall object be placed so that its image is formed at a distance of 15 cm from the lens? Also calculate the size of the image formed.
In a reading glass what is the position of the object with respect to the convex lens used?
The magnification by a lens is -3. Name the lens and state how are u and v related?
