A ray of light passes from one material into a material with a higher index of refraction. Determine whether each of the following quantities increases, decreases, or remains unchanged. HINT (a) The ray's angle with the normal. increases decreases remains unchanged (b) The light's wavelength. increases decreases remains unchanged (c) The light's frequency. increases decreases remains unchanged (d) The light's speed. increases decreases remains unchanged (e) The photon energy. increases decreases remains unchanged

a) the Angle te also decreases , b) decrease, c) unchanged , d) the speed decrease , e) unchanged

Explanation:

When a ray of light passes from one transparent material to another, it must comply with the law of refraction

     n1 sin θ₁ = n2 sin θ₂

Where index v1 is for the incident ray and index 2 for the refracted ray

With this expression let's examine the questions

a) They indicate that the refractive index increases,

      sin θ₂ = n₁ / n₂ sin θ₁

     θ₂ = sin⁻¹ (n₁ /n₂   sin θ₁)

    As m is greater than n1 the quantity on the right is less than one, the whole quantity in parentheses decreases so the Angle te also decreases

Answer is decrease

b) The wave velocity eta related to the wavelength and frequency

      v = λ f

The frequency does not change since the passage from one medium to the other is a process of forced oscillation, resonance whereby the frequency in the two mediums is the same.

The speed decreases with the indicated refraction increases and therefore the wavelength decreases

      λ = λ₀ / n

The answer is decrease

c) from the previous analysis the frequency remains unchanged

d) the refractive index is defined by

       n = c / v

So if n increases, the speed must decrease

The answer is decrease

e) the energy of the photon is given by the Planck equation

      E = h f

Since the frequency does not change, the energy does not change either

Answer remains unchanged

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