8. If the object is placed 6 cm from a concave mirror, the image distance is 12 cm. What is the
image distance if the object is moved from the original position 1 cm away from the mirror?
Answers
✴ If the object is placed 6 cm from a concave mirror, the image distance is 12 cm. What is the image distance if the object is moved from the original position 1 cm away from the mirror?
✏ The image distance is -9.3cm.
Given :-
- If the object is placed 6 cm from a concave mirror, the image distance is 12 cm.
- The original position of object is 1 cm away from the mirror.
To Find :-
- The image distance if the object is moved from the original position 1 cm away from the mirror.
Calculation :-
We have,
- Object distance (u) = - 6cm
- Image distance (v) = - 12cm
- Focal length (f) = ?
Applying mirror Formula here,
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Now, we have our focal length -4 cm .
According to the question,
if the object is moved from the original position 1 cm away from the mirror Then,
- New, Object distance = -(6 + 1) = -7
- Focal length (f) = -4
We have to find our Image distance (v).
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➡ v = - 9.3cm
Hence,our Image distance (v) is 9.3 cm, if we keep the object 1 cm away from the mirror.
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- we need to find image distance if the object is moved from the original position 1 cm away from the mirror.
Case (i):-
If the image is real in front of the mirror , then the image distance is negative.
So,
object distance (u) = - 6cm
image distance (v) = - 12cm
Focal length (f) = ?
By using mirror Formula:-
↛ 1/f = 1/ -12 + 1/-6
↛ 1/f = -1 - 2/12
↛ 1/f = -3/12
↛ 1/ f = -1/4
↛ - f = 4 f = - 4cm
Now,
if the object is moved from the original position 1 cm away from the mirror .
Then,
- Object distance = -(6 + 1) = -7cm
- Focal length (f) = -4
- image distance (v) = ?
↛1/f = 1/v + 1/u
↛ 1/v = 1/f - 1/u
→ 1/v = 1/-4 -1/-7
→ 1/v = -1/4 + 1/7
→ 1/v = (-7 + 4)/28
→ 1/v = -3/28
→ -3v = 28
→ v = 28/-3
- v = - 9.3cm
Hence,
- image distance will be -9.3cm if the object is moved from the original position 1 cm away from the mirror.
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Case (ii) :-
If the image is virtual behind the mirror, then image distance is positive,
So,
- object distance (u) = - 6cm
- image distance (v) = 12cm
- Focal length (f) = ?
- By using mirror Formula:-
↛ 1/f = 1/ 12 + 1/-6
↛ 1/f = (1 - 2)/12
↛ 1/f = -1/12
↛ 1/ f = -1/12
↛ - f = 12
- f = -12cm
if the object is moved from the original position 1 cm away from the mirror
Then,
- Object distance = -(6 + 1) = -7
- Focal length (f) = -12cm
- image distance (v) = ?
↛1/f = 1/v + 1/u
↛ 1/v = 1/f - 1/u
→ 1/v = 1/-12 -1/-7
→ 1/v = -1/12 + 1/7
→ 1/v = (-7 + 12)/84
→ 1/v = 5/84
→ 5v = 84
→ v = 84/5 v = 16.8cm
Hence,
- image distance will be 16.8cm if the object is moved from the original position 1 cm away from the mirror.
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