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An object of 8cm height is placed at a distance of 10cm from a convex mirror of radius of curvature 30 cm find the nature and position and size of the image if the object is moved away from the mirror how does the image shift.?
Most Upvoted Answer
An object of 8cm height is placed at a distance of 10cm from a convex ...
Given mirror is convex mirror
Thus
f = R/2 = 30/2 = 15cm
u = -10cm
h = 8cm
Now we have to find the nature, position and size of image
Thus using mirror equation
1/f = 1/u + 1/v
=> 1/v = 1/f -1/u
=>1/v = 1/15+1/10
=> 1/v = 25/150
=> v = 6 cm { hence image will be formed between focus and pole .
Now magnification
m = -(v/u) = (h'/h)
m = -(-6/10)
= 3/5 { it means that the image will be virtual , react and diminished.
Now again
m = h'/h
3/5 = h'/8
=> h' = 24/5 cm
hence the size of image will be 24/5cm
Thus
f = R/2 = 30/2 = 15cm
u = -10cm
h = 8cm
Now we have to find the nature, position and size of image
Thus using mirror equation
1/f = 1/u + 1/v
=> 1/v = 1/f -1/u
=>1/v = 1/15+1/10
=> 1/v = 25/150
=> v = 6 cm { hence image will be formed between focus and pole .
Now magnification
m = -(v/u) = (h'/h)
m = -(-6/10)
= 3/5 { it means that the image will be virtual , react and diminished.
Now again
m = h'/h
3/5 = h'/8
=> h' = 24/5 cm
hence the size of image will be 24/5cm
Community Answer
An object of 8cm height is placed at a distance of 10cm from a convex ...
Given:
- Height of object (h) = 8cm
- Distance of object from mirror (u) = 10cm
- Radius of curvature (R) = 30cm
To find:
- Nature (real/virtual), position (v) and size (h') of the image.
- Shift in position of the image if the object is moved away from the mirror.
Solution:
Step 1: Calculate the focal length of the mirror using the formula:
f = R/2
f = 30/2
f = 15cm
Step 2: Calculate the object distance (u) from the mirror:
u = -10 cm (as the object is placed in front of the mirror)
Step 3: Calculate the image distance (v) using the mirror formula:
1/f = 1/v + 1/u
1/15 = 1/v - 1/10
1/v = 1/15 + 1/10
1/v = 1/6
v = 6cm
Step 4: Calculate the magnification (m) of the image:
m = -v/u
m = -6/-10
m = 0.6
Step 5: Calculate the height (h') of the image using the magnification formula:
m = h'/h
0.6 = h'/8
h' = 4.8cm
Therefore, the image formed is real, inverted and diminished. Its position is 6cm from the mirror and its height is 4.8cm.
Step 6: If the object is moved away from the mirror, the image will shift as follows:
- If the object is moved further away from the mirror, the image will move closer to the mirror and its size will decrease.
- If the object is moved closer to the mirror, the image will move further away from the mirror and its size will increase.
Conclusion:
Hence, the nature, position and size of the image formed by the convex mirror have been calculated. The shift in position of the image when the object is moved away from the mirror has also been explained.
- Height of object (h) = 8cm
- Distance of object from mirror (u) = 10cm
- Radius of curvature (R) = 30cm
To find:
- Nature (real/virtual), position (v) and size (h') of the image.
- Shift in position of the image if the object is moved away from the mirror.
Solution:
Step 1: Calculate the focal length of the mirror using the formula:
f = R/2
f = 30/2
f = 15cm
Step 2: Calculate the object distance (u) from the mirror:
u = -10 cm (as the object is placed in front of the mirror)
Step 3: Calculate the image distance (v) using the mirror formula:
1/f = 1/v + 1/u
1/15 = 1/v - 1/10
1/v = 1/15 + 1/10
1/v = 1/6
v = 6cm
Step 4: Calculate the magnification (m) of the image:
m = -v/u
m = -6/-10
m = 0.6
Step 5: Calculate the height (h') of the image using the magnification formula:
m = h'/h
0.6 = h'/8
h' = 4.8cm
Therefore, the image formed is real, inverted and diminished. Its position is 6cm from the mirror and its height is 4.8cm.
Step 6: If the object is moved away from the mirror, the image will shift as follows:
- If the object is moved further away from the mirror, the image will move closer to the mirror and its size will decrease.
- If the object is moved closer to the mirror, the image will move further away from the mirror and its size will increase.
Conclusion:
Hence, the nature, position and size of the image formed by the convex mirror have been calculated. The shift in position of the image when the object is moved away from the mirror has also been explained.
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An object of 8cm height is placed at a distance of 10cm from a convex mirror of radius of curvature 30 cm find the nature and position and size of the image if the object is moved away from the mirror how does the image shift.?
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An object of 8cm height is placed at a distance of 10cm from a convex mirror of radius of curvature 30 cm find the nature and position and size of the image if the object is moved away from the mirror how does the image shift.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An object of 8cm height is placed at a distance of 10cm from a convex mirror of radius of curvature 30 cm find the nature and position and size of the image if the object is moved away from the mirror how does the image shift.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object of 8cm height is placed at a distance of 10cm from a convex mirror of radius of curvature 30 cm find the nature and position and size of the image if the object is moved away from the mirror how does the image shift.?.
An object of 8cm height is placed at a distance of 10cm from a convex mirror of radius of curvature 30 cm find the nature and position and size of the image if the object is moved away from the mirror how does the image shift.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An object of 8cm height is placed at a distance of 10cm from a convex mirror of radius of curvature 30 cm find the nature and position and size of the image if the object is moved away from the mirror how does the image shift.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An object of 8cm height is placed at a distance of 10cm from a convex mirror of radius of curvature 30 cm find the nature and position and size of the image if the object is moved away from the mirror how does the image shift.?.
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