Hi Keira!
Q11: We're lucky because they give us the formula for this question.
O is the distance from the lens to the object and I is the distance from the lens to the image. Both are given. Make sure to convert to meters.
Then,
S = 1/O + 1/I = 1/1 + 1/0.02 = 1 + 50 = 51 D (or diopters)
To figure out the 1/0.02 (which is kind of wonky), we can do a little fraction trick.
Since 0.02 is the same think as 2/100, we can rewrite this as
1/0.02 = 1/(2/100) = 1*(100/2) = 100/2 = 50
HA. Take that, math.
Q45: I will attempt an explanation! 😤
First, let's use the thin-lens equation:
1/f = 1/o + 1/i
We are TOLD that the object is at 3f, so o = 3f.
We will use this information to solve for i. Note that we cannot solve for a specific VALUE of i. Instead, we will solve for i as a function of the focal length, f.
1/f = 1/(3f) + 1/i
1/i = 1/f - 1/(3f)
Now we need a common denominator. Multiply the first term by 3/3.
1/i = 3/(3f) - 1/(3f)
Subtract.
1/i = (3 - 1)/(3f)
1/i = 2/(3f)
Flip both sides.
i = (3f)/2
Now we can use the magnification equation.
m = height of image / height of object = -i/o = -(3f)/2 / (3f)
3f's cancel, and we get -1/2.
We don't care about the negative sign. That just tells us that the image is INVERTED. What we care about is the MAGNITUDE: 1/2.
This tells us that the image is 50% the size of the object. Ooooh. 😀
The best answer is B.