Question

Calculate the angle of incidence of beam radiation on a plane surface titled by 45° from the horizontal plane and pointing 30° west of south located at mumbai at 1:30pm(IST) on 15 november .The longitude and latitude of mumbai are 72° 49` east and 18°54` north respectively .The standard longitude for IST is 81°44` east

Answer 1

Answer:

45 degree is the angle of incidence because angle of incidence is equal to angel of reflection

Answer 2

Angle of incidence  

          Angle of incidence is defined as the angle between the ray incident on a surface and the line perpendicular to the surface

Solution

From the given data      

  γ = 30°, β = 45°

  φ = +18.9° [ since latitude is positive for the northern hemisphere ]    

  Standard time = 1:30 PM = 13:30 hours

Then, Solar time = 13 hours 30 min - 4(81.733° - 72.816°) min + 14.74 min

                            = 13:9.072 hours

By assuming, δ = -19.148° , E = 14.74 min  

  hour angle, ω = -17.27° [ (12 - solar time in hours ) * 15 degrees ]

Now the angle of incidence can be calculated using  

cos $\theta_{i}$ = [ cos δ cos ω(cos φ cos β + sin φ sin β cos γ ) ] + [ cos δ sin ω sin β sin γ + sin δ (sin φ cos β - cos φ sin β cos γ) ]

Substituting the given data in the formula

cos $\theta_{i}$ = [ cos (+18.9°) cos (45°) + sin(+18.9°) sin(45°) cos (30°) ] cos(-19.148°) cos(-17.27°) + cos(-19.148°) sin(-17.27°) sin(45°) sin(30°) + sin(-19.148°) [sin(+18.9°)cos(45°)-cos(+18.9°) sin(45°) cos(30°) ]

By solving the above values,

cos $\theta_{i}$  = 0.78229 - 0.09915 + 0.11305

      $\theta_{i}$  = $cos^{-1}$ (0.79619)    

           = 37.23°

    The angle of incidence ,  $\theta_{i}$  = 37.23°