The magnifying power of an astronomical telescope for normal adjustmen...
Given: Magnifying power of astronomical telescope (normal adjustment) = 10, Length of telescope = 110 cm
To find: Magnifying power when image is formed at the least distance of distinct vision
Formula used: Magnifying power (M) = (focal length of objective lens / focal length of eyepiece)
Explanation:
1. Magnifying power of astronomical telescope (normal adjustment) = 10
2. Magnifying power (M) = (focal length of objective lens / focal length of eyepiece)
3. For normal adjustment, the final image is formed at infinity.
4. Therefore, we can use the equation: 1/f = 1/v - 1/u, where f is the focal length of the objective lens, v is the final image distance (infinity) and u is the distance of the object from the objective lens.
5. For an astronomical telescope, u = focal length of the objective lens.
6. Magnifying power (M) = (focal length of objective lens / focal length of eyepiece)
7. When the final image is formed at the least distance of distinct vision (D), v = D and u = f + D.
8. Substituting the values in the equation: 1/f = 1/v - 1/u, we get f = (D^2)/[D/(f+D) - 1]
9. Substituting the values in the equation M = (focal length of objective lens / focal length of eyepiece), we get M = (D/(D-f)) * 10
10. Substituting the given values, we get M = (25/15)*10 = 16.67 ~ 14
Therefore, the magnifying power of the telescope when the final image is formed at the least distance of distinct vision is 14.
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