Coming Out The Same Way

A glass prism whose cross-section is an isosceles triangle stands with its (horizontal) base in water; the angles that its two equal sides make with the base are each \(\theta\).

An incident ray of light, above and parallel to the water surface and perpendicular to the prism's axis, enters the prism and is internally reflected at the glass-water interface and re-emerges into the air. Taking the refractive indices of glass and water to be \(\frac{3}{2}\) and \(\frac{4}{3}\), respectively.

Calculate the minimum value of \(\theta\) (in radians) for total internal reflection to be possible.

Give your answer to 3 decimal places.

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