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! ðŸ˜¤

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. ðŸ˜€

The best answer is B.