One light wave is incident upon a plate of refracting index`mu`.incident angle`i`,for with refractive &refelctive waves are mutually perpendicular will be
(1) `i=45^(@)` (ii)`i=sin^(-1)(mu)` (iii)`i="cosec"^(-1)(mu)` (iv)`i=tan^(-1)(mu)`

Explanation

To solve the problem, we need to determine the incident angle \( i \) at which the refracted wave and the reflected wave are mutually perpendicular. Let's go through the steps systematically.

### Step 1: Understanding the Geometry
When a light wave is incident on a plate, it can be reflected and refracted. The angle of incidence is \( i \), the angle of reflection is also \( i \) (according to the law of reflection), and the angle of refraction is \( r \).

### Step 2: Setting Up the Relationship
According to the problem, the reflected wave and the refracted wave are perpendicular to each other. This means that the angle between them is \( 90^\circ \). Therefore, we can write the relationship:
\[
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