A convex lens of focal length 30cm form image three times enlarged on a screen calculat distance of object distance of image and nature of image
Answers
Answer
- Object is placed at 40 cm in front of the lens
- Image is formed at 120 cm behind the lens
- Nature of image: Real and inverted
Explanation
Given:-
- The focal length of the convex lens is 30 cm
- An image is formed that is obtained on the screen
- The image formed is three times enlarged
To find:-
- Position of the object, u =?
- Position of the image, v =?
- Nature of image
Formulae required:-
- The Formula for magnification of the lens
m = v / u
- Lens formula
1 / f = 1 / v - 1 / u
[ Where m is magnification, f is focal length, v is the position of image and u is the position of object ]
Solution:-
The focal length of a convex lens is always positive, so
- the focal length of the convex lens, f = 30 cm
Since image formed is obtained on screen it means image formed is real. so the magnification of the lens will be negative.
- magnification, m = -3
Let, the position of the image be v and position of the object be u
Using the formula for magnification of the lens
→ m = v / u
→ -3 = v / u
→ v = -3 u ......equation (1)
Now, Using lens formula
→ 1 / f = 1 / v - 1 / u
→ 1 / 30 = 1 / v - 1 / u
[ Using equation (1) ]
→ 1 / 30 = 1 / ( -3 u) - 1 / u
→ 1 / 30 = ( - 1 - 3 ) / ( 3 u )
→ 1 / 30 = -4 / 3u
→ 3 u = -4 × 30
→ u = -40 cm
Putting value of u in equation (1)
→ v = -3 u
→ v = -3 × -40
→ v = 120 cm
Hence,
- Position of the object is 40 cm in front of the lens
- Position of the image is 120 cm behind the lens
- The image formed is real and inverted in nature.
Answer:
Answer
Object is placed at 40 cm in front of the lens
Image is formed at 120 cm behind the lens
Nature of image: Real and inverted
Explanation
Given:-
The focal length of the convex lens is 30 cm
An image is formed that is obtained on the screen
The image formed is three times enlarged
To find:-
Position of the object, u =?
Position of the image, v =?
Nature of image
Formulae required:-
The Formula for magnification of the lens
m = v / u
Lens formula
1 / f = 1 / v - 1 / u
[ Where m is magnification, f is focal length, v is the position of image and u is the position of object ]
Solution:-
The focal length of a convex lens is always positive, so
the focal length of the convex lens, f = 30 cm
Since image formed is obtained on screen it means image formed is real. so the magnification of the lens will be negative.
magnification, m = -3
Let, the position of the image be v and position of the object be u
Using the formula for magnification of the lens
→ m = v / u
→ -3 = v / u
→ v = -3 u ......equation (1)
Now, Using lens formula
→ 1 / f = 1 / v - 1 / u
→ 1 / 30 = 1 / v - 1 / u
[ Using equation (1) ]
→ 1 / 30 = 1 / ( -3 u) - 1 / u
→ 1 / 30 = ( - 1 - 3 ) / ( 3 u )
→ 1 / 30 = -4 / 3u
→ 3 u = -4 × 30
→ u = -40 cm
Putting value of u in equation (1)
→ v = -3 u
→ v = -3 × -40
→ v = 120 cm
Hence,
Position of the object is 40 cm in front of the lens
Position of the image is 120 cm behind the lens
The image formed is real and inverted in nature.
Explanation: