Given : ‌a‌µw=‌

4

3

, Shift =3.0‌mm.
Let the real depth of the coin in water be
=′x‌ ' ‌mm
∴ Apparent depth of the coin =(x−3)‌mm.
We know,
‌a‌µw=‌

‌ Real depth ‌

‌ Apparent depth ‌

∴‌‌‌

4

3

‌=‌

x

(x−3)

⇒4(x−3)‌=3x
⇒4x−12‌=3x
⇒4x−3x‌=12
⇒‌‌x=12‌mm‌ or ‌1.2‌cm
∴ Real depth of the coin in water
=12‌mm‌ or ‌1.2‌cm‌. ‌