an object 5cm lenght is placed at distance of 20cm in front of a convex mirror of radius of curvature 30 cm . find the position of the image
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To find the position of the image formed by the convex 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 image distance (distance of the image from the mirror)
- u is the object distance (distance of the object from the mirror)
In this case, the object distance u is given as 20 cm, and the convex mirror has a radius of curvature of 30 cm. To determine the focal length of the convex mirror, we can use the relation:
f = R/2
where R is the radius of curvature. Plugging in the given value, we find:
f = 30 cm / 2 = 15 cm
Now, we can substitute the given values into the mirror formula and solve for v:
1/15 = 1/v - 1/20
To solve this equation, we can use the concept of algebraic manipulation:
1/v = 1/15 + 1/20
Combining the fractions on the right side:
1/v = (4 + 3)/60
1/v = 7/60
Flipping both sides:
v = 60/7 cm
Therefore, the position of the image formed by the convex mirror is approximately 8.57 cm in front of the mirror.