Double Slit Problem: Solving Unknown Wavelength

[pari786]

Homework Statement

A double slit is illuminated simultaneously with orange light of wavelength 600nm and light of an unknown wavelength. the m=4 bright fringe of the unknown wavelength overlaps the m=3 bright orange fringe. What is the unknown wavelength?

Homework Equations

dsin(theta) = m(lambda)

The Attempt at a Solution

I tried finding d for orange light by suing the above formula. I substitued m=3
sin 90 and wavelength as 600 x 10^-9
and got d= 0.0000018m
and then I used this d to find unknown wavelength and used the same above equation but this time substitutes m=4 and sin120 and got wavelength= 0.000000389m or (389nm)

but my answer is wrong ... please tell me where I'm making mistake.

 

[chaoseverlasting]

Why did you use sin90 in the first case and sin 120 in the second? We don't know what angle the rays make with the axis.
Since its given that 3rd fringe of the orange light is equal to the 4th fringe of the unknown wavelength, here the angle both rays (of different wavelengths) make with the axis is the same.
Therefore, here, dsin(theta) is a constant.
Thus, 3*600nm=4*x, giving the unknown wavelength to be 450nm.

 

[pari786]

Why did you use sin90 in the first case and sin 120 in the second? We don't know what angle the rays make with the axis.
Since its given that 3rd fringe of the orange light is equal to the 4th fringe of the unknown wavelength, here the angle both rays (of different wavelengths) make with the axis is the same.
Therefore, here, dsin(theta) is a constant.
Thus, 3*600nm=4*x, giving the unknown wavelength to be 450nm.

Yeah, I realized later on that angles are wrong ... I used
(delta)r = m(wavelength)
first I found the delta r quantity for orange light by substituting m=3 and wavelength = 600*10^-9m

and I got Delta r = 0.0000018 m and then I used the same equation but different value of m =4 (given in the question)
I got the same wavelength 450nm.

But thanks for the help.