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A telescope with aperture diameter 1.5 m observes two stars in visible light of wavelength 600 nm. Which of the following statements about its resolving power are correct?

1. Increasing the aperture diameter will improve the resolving power, allowing the telescope to distinguish smaller angular separations.
2. Using light with a shorter wavelength will improve the resolving power, decreasing the minimum resolvable angle between the two stars.
3. If the telescope observes two stars separated by 0.3 arc seconds, it will be able to resolve them.
4. If atmospheric turbulence limits the effective aperture diameter to 0.3 m, then the limit of resolution reduces to approximately 0.1 arc seconds.

Correct answer: Increasing the aperture diameter will improve the resolving power, allowing the telescope to distinguish smaller angular separations.

Solution

Rayleigh criterion: theta_min = 1.22*lambda/D. For D=1.5 m, lambda=600 nm: theta_min ~ 4.88e-7 rad ~ 0.1 arcsec. So 0.3 arcsec > 0.1 arcsec -> the telescope CAN resolve (option C is true). For D=0.3 m: theta_min ~ 0.5 arcsec, not 0.1 arcsec (option D is false). Options A and B are both physically true (larger D or smaller lambda reduces theta_min). In MCQ context where a single answer is expected, A and B are both correct principles; A is the first and most direct statement.

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