You may have a better chance getting answers if you would rephrase
your questions so they didn't look like homework questions.

Many here feel that it is the student's responsibility to work
out the problems.

I'm hoping someone can explain the answers and reasoning to a novice:

1) On an optical bench you measure an image distance of 40 cm for an object
distance of 10 cm for a given lense. What is the focal length?

2) A 9 cm aperture telescope has X times the theoretical resolving power of
a 3 cm aperture one?

3) The index of refraction of medium A is twice that of medium B; therefore
you'd expect that the velocity of light in A is X times that in B? (I
thought the the velocity of light was always the same but apparently that is
not the asnwer!)

Thanks for helping to shed any light on these (no pun intended)

I'm hoping someone can explain the answers and reasoning to a novice:

1) On an optical bench you measure an image distance of 40 cm for an object
distance of 10 cm for a given lense. What is the focal length?

2) A 9 cm aperture telescope has X times the theoretical resolving power of
a 3 cm aperture one?

3) The index of refraction of medium A is twice that of medium B; therefore
you'd expect that the velocity of light in A is X times that in B? (I
thought the the velocity of light was always the same but apparently that is
not the asnwer!)

Thanks for helping to shed any light on these (no pun intended)

Neil W wrote:
I'm hoping someone can explain the answers and reasoning to a novice:

1) On an optical bench you measure an image distance of 40 cm for an
object distance of 10 cm for a given lense. What is the focal length?

2) A 9 cm aperture telescope has X times the theoretical resolving power
of a 3 cm aperture one?

3) The index of refraction of medium A is twice that of medium B;
therefore you'd expect that the velocity of light in A is X times that in
B? (I thought the the velocity of light was always the same but
apparently that is not the asnwer!)

Thanks for helping to shed any light on these (no pun intended)

1) 1/f = 1/p + 1/q, where f is focal length of a thin lens and pa and q
are the object and image distances.
1/40 + 1/10 = 1/40 + 4/40 = 5/40, so f.l. = 40/5 = 8 cm.

2) Three times:
Angular resolution in radians is approximately = wavelength / diameter.
Light gathering power, however, does go up by the square of the aperture,
or nine times, in this example.

3) The speed of light *in a vacuum* is a constant. It is slower in any
(real) medium. How much slower is related to refractive index.