Suppose that the spotlight shines so that different parts of the beam reflect off of different two surfaces, one inclined at an angle α (from the horizontal) and one inclined at an angle β. What would the angular separation Δθ be between the rays reflected from the two surfaces? Assume that the light comes at an angle θa to the vertical. Express your answer in terms of some or all of the angles θa, α, and β.

Sasha has just gotten a new job in a nearby city. after comparison shopping, she found that renting a nice two-bedroom apartment would cost around $800 per month. her utilities would cost about $150 per month. sasha has enough money saved for a down payment, and she found that she can buy a three-bedroom house or condo with a mortgage payment of $1,000 per month, including taxes and homeowner's insurance. her utilities would cost about $200 per month. what is the advantage of buying the house over renting the apartment?