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find the approximate distance between the images of two stars, which are just resolved by a lens of focal length 3m and diameter 10 cm. assume a wavelength of 550 nm.

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Final answer:

The approximate distance between the images of two stars that are just resolved by a lens can be found using the formula for angular resolution. In this case, the distance is approximately 3.19 cm.

Step-by-step explanation:

The distance between the images of two stars that are just resolved by a lens can be determined using the concept of angular resolution.

The formula for calculating the angular resolution is given by θ = 1.22 * (λ/D), where θ is the angular resolution, λ is the wavelength of light, and D is the diameter of the lens.

In this case, the focal length of the lens is not needed to find the distance between the images.

Given that the diameter of the lens is 10 cm (0.1 m) and the wavelength of light is 550 nm (0.00055 m), we can substitute these values into the formula to find the angular resolution.

θ = 1.22 * (0.00055/0.1) = 0.00671 radians.

To find the approximate distance between the images of the two stars, we can use the formula

distance = focal length * tan(θ/2).

Substituting the values, the distance ≈ 3 * tan(0.00671/2).

Calculating this value gives us a distance of approximately 0.0319 m or 3.19 cm.

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