The Sun subtends an angle of 0.533° at a distance of 1 astronomical unit, which is 1.496 ✕ 1011 m, the average Sun–Earth distance. (a) What is the position (in m) of an image of the Sun at Earth's surface formed by a concave spherical mirror with a radius of curvature of magnitude 2.70 m? (Give your answers with respect to the mirror.) (b) What is the diameter (in cm) of an image of the Sun at Earth's surface formed by a concave spherical mirror with a radius of curvature of magnitude 2.70 m?
The Sun subtends an angle of 0.533° at a distance of 1 astronomical unit, which is 1.496 ✕ 1011 m, the average Sun–Earth distance. (a) What is the position (in m) of an image of the Sun at Earth's surface formed by a concave spherical mirror with a radius of curvature of magnitude 2.70 m? (Give your answers with respect to the mirror.) (b) What is the diameter (in cm) of an image of the Sun at Earth's surface formed by a concave spherical mirror with a radius of curvature of magnitude 2.70 m?
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Question
The Sun subtends an angle of 0.533° at a distance of 1 astronomical unit, which is 1.496 ✕ 1011 m, the average Sun–Earth distance.
(a)
What is the position (in m) of an image of the Sun at Earth's surface formed by a concave spherical mirror with a radius of curvature of magnitude 2.70 m? (Give your answers with respect to the mirror.)
(b)
What is the diameter (in cm) of an image of the Sun at Earth's surface formed by a concave spherical mirror with a radius of curvature of magnitude 2.70 m?
Expert Solution
Given data
- The subtended angle by the Sun is,
- The radius of a concave spherical mirror is,
Step 1
(a)
Since the Sun subtends an angle of 0.533° at a distance of 1 astronomical unit, then the image of the Sun at Earth's surface formed at the focus point (f) of the concave spherical mirror. So, the expression to calculate the distance of the image with respect to the mirror can be calculated as,
Hence, the position of the image with respect to the mirror is
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