4. The intensity I of a laser in an absorbing medium decreases exponentially with distance z from theinterfaceas I(z)=I initial(e^(-z/L) ,whereListhespaceconstant(orpenetrationdepth),andI0 istheinitial intensity (at distance zero from the interface). (a) To what exact percentage of its initial value does the intensity drop within the distance z=L, and to what percentage at z=2L and z=3L? (b) If L=0.5mm, at what distance z has the laser intensity dropped to 50% of its initial value?

Question

4.	The intensity I of a laser in an absorbing medium decreases exponentially with distance z from theinterfaceas I(z)=I initial(e^(-z/L) ,whereListhespaceconstant(orpenetrationdepth),andI0 istheinitial intensity (at distance zero from the interface). (a) To what exact percentage of its initial value does the intensity drop within the distance z=L, and to what percentage at z=2L and z=3L? (b) If L=0.5mm, at what distance z has the laser intensity dropped to 50% of its initial value?