an object is placed 10 cm from a concave spherical mirror whose radius of curvature is 12 cm. What is the distance of image
a) 5cm
b) 10 cm
c)15cm
d)20cm
e)24cm
The focal length is f = R/2 = 6 cm.
1/do + 1/di = 1/10 + 1/di = 1/6
1/di = 1/6 - 1/10 = 5/30 -3/30
= 1/15
image distance di = 15 cm
object distance do = 10 cm
To find the distance of the image formed by a concave spherical mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = distance of the image from the mirror
u = distance of the object from the mirror
In this case, we are given:
u = -10 cm (since the object is placed in front of the mirror, the distance is negative)
f = radius of curvature / 2 = 12 cm / 2 = 6 cm
Substituting these values into the formula, we get:
1/6 = 1/v - 1/-10
To simplify the equation, we can take the reciprocal of both sides:
6 = v - 6/10
Multiplying through by 10 to clear the fraction:
60 = 10v - 6
Simplifying further:
10v = 66
Dividing by 10:
v = 6.6 cm
Therefore, the distance of the image formed by the concave spherical mirror is approximately 6.6 cm.
None of the given options matches the calculated value of 6.6 cm.
To determine the distance of the image formed by a concave spherical mirror, we can use the mirror formula:
1/f = 1/v - 1/u
where:
f = focal length of the mirror (half the radius of curvature)
v = distance of the image from the mirror
u = distance of the object from the mirror
Given:
Radius of curvature, R = 12 cm
Object distance, u = 10 cm
The focal length can be calculated as:
f = R/2 = 12 cm / 2 = 6 cm
Substituting these values into the mirror formula:
1/6 = 1/v - 1/10
To solve for v, we can rearrange the equation:
1/v = 1/6 + 1/10
1/v = (5 + 3)/30
1/v = 8/30
To get v, take the reciprocal of both sides:
v = 30/8
v ≈ 3.75 cm
Therefore, the distance of the image is approximately 3.75 cm. None of the provided options match, so none of the given choices (a), (b), (c), (d), or (e) are correct.