What two conditions are required for total internal reflection?

State the critical angle formula for light going from \(n_1\) to \(n_2\), where \(n_1>n_2\).

Find the critical angle for glass \((n=1.50)\) to air \((n=1.00)\).

Light in glass \((n=1.50)\) reaches an air boundary at \(50^\circ\). Does total internal reflection occur?

Light travels from water \((n=1.33)\) to air. Find the critical angle.

Can total internal reflection occur when light travels from air into glass? Explain.

At the critical angle, what is the refracted angle?

A transparent material has critical angle \(35.0^\circ\) at an air boundary. Find its refractive index.

Derive the critical angle formula from Snell's law.

An optical fiber core has \(n=1.48\) and cladding has \(n=1.46\). Find the critical angle at the core-cladding boundary and explain why the angle is large.

Diamond has \(n=2.42\). Find its critical angle at a diamond-air boundary.

A ray inside glass \((n=1.50)\) hits a glass-air boundary at \(40^\circ\). Does it refract or totally internally reflect?

For glass \((n=1.50)\) to air, find the refracted angle when the incident angle is \(40^\circ\).

A material has critical angle \(60^\circ\) at an air boundary. Find its refractive index.

A ray travels inside a fiber core \((n=1.50)\) surrounded by cladding \((n=1.45)\). The ray makes \(12^\circ\) with the fiber axis. Assuming the wall is parallel to the axis, does it totally internally reflect at the core-cladding boundary?

Derive the largest ray angle to the fiber axis for total internal reflection inside a straight fiber with core index \(n_1\) and cladding index \(n_2\).

For a fiber with \(n_1=1.50\) and \(n_2=1.45\), find the largest internal ray angle to the fiber axis that still totally internally reflects.

Use Snell's law to show why no real refracted angle exists beyond the critical angle.

A glass prism in air is used so a ray inside the prism hits a face at \(45^\circ\). If the glass has \(n=1.52\), determine whether total internal reflection occurs.

Explain why total internal reflection can be nearly lossless even though ordinary reflection from glass can be weak.