If the refractive index of the ice with respect to air is 1.31 and that of rock salt is 1.54. The refractive index of rock salt with respect to ice is _______.

The refractive index of the ice with respect to air = 1.31. 

$\frac{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{air}}{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{ice}}=1.31$ ……..(1)
Refractive index of the rock salt with respect to air $=\mathit{ }1.54$
$\frac{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{air}}{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{rock}\mathrm{salt}}=1.54$ ……..(2)
Refractive index of the rock salt with respect to ice =$\frac{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{ice}}{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{rocksalt}}$
Dividing equation (2) by equation (1)
$\Rightarrow$   $\frac{\frac{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{air}}{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{rocksalt}}}{{\displaystyle \frac{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{air}}{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{ice}}}}=\frac{1.54}{1.31}$

  $\Rightarrow \frac{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{ice}}{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{rock}\mathrm{salt}}=1.18\mathrm{ }$

Therefore, the refractive index of the rock salt with respect to ice = 1.18