If I want to reflect sunlight by using concave mirror which had 10cm*10cm size, how much the focal length of concave mirror should be designed in order to obtain 1.5 times light reflection size which had 15cm*15cm?

1/f = 1/o + 1/i

f = focal length
o = object distance (10cm)
i = image distance (15cm)

Plug in the known values.

1/f = 1/10cm + 1/15cm . . .

(You do the rest.)

Edited June 21, 20232 yr by Alysdexic

3 minutes ago, Alysdexic said:

1/f = 1/o + 1/i

f = focal length
o = object distance (10cm)
i = image distance (15cm)

Plug in the known values.

1/f = 1/10cm + 1/15cm . . .

(You do the rest.)

The OP did not say anything about object/image distance. Rather about mirror/reflection size.

9 minutes ago, Genady said:

The OP did not say anything about object/image distance. Rather about mirror/reflection size.

So why don't you answer them instead of replying to me?

OP:

10cm x 10cm
15cm x 15cm (1.5 times larger)

f = r^2 / 4s

f = focal length
r = radius of the mirror / 10cm (half the mirror's diameter)
s = enlargement ratio / 1.5 (50% enlargement)

f = (10cm)^2 / 4(1.5), etc.

4 minutes ago, Alysdexic said:

So why don't you answer them

Because it is impossible to give a meaningful answer to the OP's question.
 

 

4 minutes ago, Alysdexic said:

instead of replying to me?

Because it is potentially helpful to you if we point out that your reply, while well intended, was wrong.