Show that if lambda be the angle of friction and mu the coefficient of static friction then lambda is < = tan ^-1 mu.

See the following figure for reference:

Here f = limiting frictional force

F = applied force

λ = angle of friction

mg = downward weight

R = reaction force.

Angle of friction is defined as the angle between the direction of the resultant of reaction force and frictional force with the reaction force. As you can see in the given fig. We know,

Now, in ΔACB:

As this is for limiting friction case. For motion to occur,