How is refractive index relate to the angle of bending of light?

Question

Nathan Ashcroft · Accepted Answer

You can use the Snell's law to judge that,

Suppose light falls at air - object interface,the object has a refractive index #mu>1#,so if the angle of incidence is #theta#, and angle of refraction is #phi#,then using Snell's law,

#sin theta = mu sin phi#

or,# sin phi = 1/(mu) sin theta#

Now, #sin theta# is constant, so higher the value of #mu#,lower is the value of #sin phi# and lower is the value of #phi#,and here more bending means,less value of #phi#,see the diagram to get how #phi# is calculated.

Charles Aeschliman · Answer

undefined The angle of bending of light is related to the refractive index through Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media, which is also equal to the ratio of the refractive indices of the two media. Mathematically, it can be expressed as:

$$ \frac{\sin(\theta_1)}{\sin(\theta_2)} = \frac{v_1}{v_2} = \frac{n_2}{n_1} $$

where:
- $ \theta_1 $ is the angle of incidence,
- $ \theta_2 $ is the angle of refraction,
- $ v_1 $ and $ v_2 $ are the speeds of light in the first and second media, respectively,
- $ n_1 $ and $ n_2 $ are the refractive indices of the first and second media, respectively.