To solve this problem it is necessary to apply the concepts related to the principle of superposition and the equations of destructive and constructive interference.
Constructive interference can be defined as

Where
m= Any integer which represent the number of repetition of spectrum
= Wavelength
d = Distance between the slits.
= Angle between the difraccion paterns and the source of light
Re-arrange to find the distance between the slits we have,



Therefore the number of lines per millimeter would be given as



Therefore the number of the lines from the grating to the center of the diffraction pattern are 380lines per mm
Answer:
Work done, W = 1786.17J
Explanation:
The question says "A 75.0-kg painter climbs a 2.75-m ladder that is leaning against a vertical wall. The ladder makes an angle of 30.0 ° with the wall. How much work (in Joules) does gravity do on the painter? "
Mass of a painter, m = 75 kg
He climbs 2.75-m ladder that is leaning against a vertical wall.
The ladder makes an angle of 30 degrees with the wall.
We need to find the work done by the gravity on the painter.
The angle between the weight of the painter and the displacement is :
θ = 180 - 30
= 150°
The work done by the gravity is given by :

Hence, the required work done is 1786.17 J.
Mathematically, relation between force, area and pressure is given by...
Pressure = force / area
hence, pressure is directly proportional to force but inversely proportional to area.
Average speed=total distance traveled/time. Total distance=the sum of the two short distances=79*2+77*3=389 km. Total time used to travel is 2+3=5 hr. Average speed is 389/5=77.8 km/hr.