Question

Derive an expression for apparent depth when the object is placed in denser medium and observer in rarer medium. pls a answer fast​.

Answer 1

Expression for Apparent Depth:

• Let's assume that a coin has been placed at an actual depth of 'd' (at the bottom of the container). The observer is present in the rarer media.

• Let d' be apparent depth and d be actual depth.

Now, refer to diagram:

Applying Snells's Law:

$\mu \sin(i) = 1 \times \sin(r)$

$\implies\mu = \dfrac{ \sin(r) }{ \sin(i) }$

For very small angles, sin can be changed to tan:

$\implies\mu = \dfrac{ \tan(r) }{ \tan(i) }$

$\implies\mu = \dfrac{( \frac{x}{d'} )}{( \frac{x}{d} ) }$

$\implies\mu = \dfrac{d}{d'}$

$\boxed{ \implies d' = \dfrac{d}{ \mu}}$

Hope It Helps.