a converging mirror of focal length 20cm forms an image which is twice the size of the object .calculate two possible distances of the object from the mirror?
To calculate the two possible distances of the object from the converging mirror, we can use the mirror formula:
1/f = 1/v - 1/u,
where f is the focal length of the mirror, v is the distance of the image from the mirror, and u is the distance of the object from the mirror.
Given that the focal length (f) is 20cm and the image (v) is twice the size of the object, we can determine the image distance:
Let the distance of the object from the mirror be u.
Since the image is twice the size of the object, we have:
v = 2u.
Substituting these values into the mirror formula, we get:
1/20 = 1/(2u) - 1/u.
We can simplify this equation:
1/20 = (1 - 2)/(2u).
1/20 = -1/(2u).
To proceed, we need to find the common denominator:
1/20 = -1/(2u) * 20/20.
1/20 = -20/(40u).
Now, we can solve for u:
1 = -20/(40u).
Cross-multiplying, we get:
40u = -20.
Dividing both sides by 40, we find:
u = -20/40.
Therefore, one possible distance of the object from the mirror is u = -0.5 cm.
To find the second distance, we need to consider that the distance of the object from the mirror cannot be negative. Thus, we take the positive value of u:
u = 0.5 cm.
Therefore, the two possible distances of the object from the mirror are u = 0.5 cm and u = -0.5 cm, respectively.