Differentiate angle of repose and angle …

Angle of Friction beween any two surface in contact is defined as the angle which the resultant

of the force of limiting friction F_lim and normal reaction N makes with the direction of normal reaction N

as shown in figure. It is marked in the figure as θ.

The value of angle of friction depends on the material and nature of surfaces in contact. 

It can be seen from figure, tanθ = AC/OA = F_lim / N = μ , where μ is coefficient of limiting friction

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The angle of repose or angle of sliding  α is defined as the minimum angle of inclination of a plane

with the horizontal such that a body placed on the plane just begins to slide down.

Its value depends on the material and nature of the surface in contact. 

from the figure it can be seen that, f =mg sinα ...............(1)
N = mg cosα ....................(2)

hence we get,  f / N = tan α = μ