An object is placed 12 cm in front of a lens with a focal length of 8.0 cm.(i) (2 marks)Calculate the image distance.(ii) (2 marks)Sketch a ray diagram of the image, and lens, showing at least the three principal rays. You may include more relevant rays if you wish.

(i) To calculate the image distance, we can use the lens formula which is 1/f = 1/v - 1/u. Here, f is the focal length, v is the image distance, and u is the object distance.

Given: f = 8.0 cm (focal length) u = -12 cm (object distance is negative as it is on the same side as light is coming from)

We can substitute these values into the lens formula:

1/f = 1/v - 1/u 1/8 = 1/v - 1/(-12) 1/8 = 1/v + 1/12

To solve for v, we first get a common denominator and combine the fractions:

3/24 = 1/v + 2/24 1/v = 3/24 - 2/24 1/v = 1/24

Finally, we take the reciprocal of both sides to solve for v:

v = 24 cm

So, the image distance is 24 cm.

(ii) As a text-based AI, I'm unable to sketch a ray diagram. However, I can explain how to do it:

1. Draw a straight horizontal line to represent the principal axis.
2. Draw a vertical line in the middle of the principal axis to represent the lens.
3. Mark the focal point (F) on both sides of the lens at 8 cm from the lens.
4. Draw an object as an upright arrow on the left side of the lens at 12 cm from the lens.
5. Draw three principal rays:
   • Ray 1: Draw a straight line from the top of the object passing through the lens. This ray goes straight through the lens without bending.
   • Ray 2: Draw a line from the top of the object through the focal point on the right side of the lens. After passing through the lens, this ray will go parallel to the principal axis.
   • Ray 3: Draw a line from the top of the object parallel to the principal axis. After passing through the lens, this ray will go