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A concave mirror is designed so that an object 1.0 m in

front of it produces a real image at a distance of 1.6 m in
front of the mirror. What is the radius of curvature of the
mirror?

User M Granja
by
8.3k points

1 Answer

7 votes

Answer:

We can use the mirror equation to find the radius of curvature of the mirror.

The mirror equation is:

1/f = 1/d₀ + 1/dᵢ

where f is the focal length of the mirror, d₀ is the object distance, and dᵢ is the image distance.

In this problem, we are given:

d₀ = 1.0 m

dᵢ = 1.6 m

We need to find f, and then we can use the relationship between f and the radius of curvature R to find R.

From the mirror equation, we can rearrange to solve for f:

1/f = 1/d₀ + 1/dᵢ

1/f = 1/1.0 + 1/1.6

1/f = 1.6/1.0 * 1/2.6

f = 0.615 m

Now, we can use the relationship between f and R to find R:

f = R/2

R = 2f = 2 * 0.615 m = 1.23 m

Therefore, the radius of curvature of the concave mirror is 1.23 m.

User Christian Fries
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