An object 5 cm in size is placed at 12 CM in front of a concave mirror of radius of curvature of 20 CM at what distance from the mirror should a screen be placed in order to obtain a sharp image? find the nature and size of the L .
Answers
Given :-
- Height of the image {h_(1)} = 5cm
- The distance of object (u) = - 12cm
- The radius of curvature (r/2) = 20cm
- The focal length of the object = -20/2 = - 10cm
To Find :-
- The nature and size of image = ?
Solution :-
To calculate the nature and size of image at first we have to calculate the distance from the mirror should a screen be placed in order to obtain a image (v). By Applying formula we can calculate (v) then calculate the nature and the size of image.
By using mirror formula :-
⇢ 1/v + 1/u = 1/f
⇢ 1/v + 1/-12 = 1/-10
⇢ 1/v = -1/10 + 1/12
⇢ 1/v = (-6 + 5)/60
⇢ 1/v = -1/60
⇢ v = - 60cm
Therefore, the screen should be placed at 20cm in front of the centre of curvature to obtain the image.
Calculation for size of image :-
⇢ magnification (m) = h_2/h_1 = -v/u
⇢ magnification (m) = h_2/5 = -(-60)/-12
⇢ magnification (m) = h_2 = 5 × 60/-12
⇢ magnification (m) = h_2 = 300/-12
⇢ magnification (m) = h_2 = -25cm
Therefore , the size of the image h_2 = - 25cm
As above you can see that image obtained with negative the sign so, the nature of image be inverted.
Answer:
Question :-
- An object 5 cm in size is placed at 12 CM in front of a concave mirror of radius of curvature of 20 CM at what distance from the mirror should a screen be placed in order to obtain a sharp image? find the nature and size of the L .
Given :-
- An object 5 cm in size is placed at 12 CM in front of a concave mirror of radius of curvature of 20 CM.
Find Out :-
- At what distance from the mirror should a screen be placed in order to obtain a sharp image?
- Find the nature and size of the L .
Solution :-
☣ Image Distance :
We have :
- Object Distance = - 12 cm
- Focal Length = = - 10 cm
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☣ Size of Image :
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Henceforth, the mirror should a screen be placed in order to obtain a sharp image is 20 cm.
The size of the image is 8.33 cm.
The nature of the image is inverted.
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Image Distance :
- The image distance always equals the object distance.
- The size of the image is the same as the object (the mirror does not magnify the image).
Object Distance :
- The distance between the point of incidence and the object placed in front of a mirror is called object distance.
- The image is the same distance behind the mirror as the object is in front of the mirror.
Focal Length :
- The focal length ( f ) is the distance from a lens or mirror to the focal point ( F ).
- This is the distance from a lens or mirror at which parallel light rays will meet.