Question

Solve Numerical example.

A glass slab of thickness 2.5 cm having refractive index 5/3 is kept on an ink spot. A transparent beaker of very thin bottom, containing water of refractive index 4/3 up to 8 cm, is kept on the glass block. Calculate apparent depth of the ink spot when seen from the outside air.

Answer 1

When observed from the outside air, the light coming from the ink spot gets refracted twice; once through the glass and once through the water.
∴ When observed from water,

`"n"_"g"/"n"_"w"="Real depth"/"Apparent depth"`

∴ `(5//3)/(4//3)=2.5/"Apparent depth"`

∴ Apparent depth = `2.5/(5//4)`

∴ Apparent depth = 2 cm
Now when observed from outside air, the total real depth of ink spot can be taken as (8 + 2) cm = 10 cm.

∴`"n"_"w"/"n"_"air"="Real depth"/"Apparent depth"`

∴ Apparent depth = `10/(4//3)`

= `(10xx3)/4` = 7.5 cm

Apparent depth of the ink spot when seen from the outside air is 7.5 cm.