An object is embedded in a block of ice, 10 cm below the plane surface. if the refractive index of the ice is 1.50, the apparent depth below the surface is?

Analyze the question: An object is 10 cm deep in ice (real depth) and we are asked for the apparent depth when viewed from above, given n = 1.50.

Concept: When you look into a denser medium from a less dense one (e.g., air), the object appears closer to the surface than it really is. The relationship is:

n = real depth / apparent depth

so

apparent depth = real depth / n

Solution:

• Real depth = 10 cm
• n = 1.50

Apparent depth = 10 / 1.50 = 6.67 cm

Check against the options: 6.67 cm matches option B.

(Option C, 7.50 cm, would come from a wrong calculation, and option A would come from dividing incorrectly. The apparent depth must always be less than the real depth when n > 1, and 6.67 cm satisfies this.)

Tip: Remember "apparent depth is smaller", so you always divide the real depth by n. A swimming pool looks shallower than it really is, which is the same idea. If your answer is bigger than the real depth, you've multiplied by mistake.