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**1. Homework Statement**

Question:Imagine you are in a massive desert. There is a tower of height H. A light source at the top of the tower can emit light in all directions. You are a person whose eyes are at a height h (h<H) above the ground. The refractive index of the air varies as μ=kd where k is a positive constant and d is the distance above the ground.

Question:

- What is the minimum distance at which you will still be able to see the mirage.
- What is the minimum possible distance between you and the mirage.
- If the ray starts off making an angle α below the horizontal what is the condition that a mirage is created

**I started off by assuming an element of height dx at an elevation x above the ground. Then I assumed that the ray of light is incident at an angle of θ and that the angle of refraction isθ+dθ. the refractive index changes from μ(x+dx) to μ(x). So,**

2. Homework Equations :

snell's law

2. The attempt at a solution

My approach:

2. Homework Equations :

snell's law

2. The attempt at a solution

My approach:

μ(x+dx)⋅sin(θ)=μ(x)⋅sin(θ+dθ)

Solving this gave me weird results. I think it was because I was unable to incorporate Total Internal Reflection into it.

If somebody could either point me in the right direction for solving the question or point out an error (if there is one) in the question (because I made the question myself) then I would be grateful.

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