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Homework Statement -Find the sum of the two quantities: Y1=sin(Wt) Y2=sin(Wt+30 degrees) Homework Equations Y(x,t)=AsinK(kx+Wt) <------- not sure if this is relevant W=2(3.14)f , where f=frequency The Attempt at a Solution sin(Wt) + sin(Wt+30) = sin(Wt) + sin(Wt) +...
2. Optics problem involving a converging lens

Homework Statement An Object and a screen are located a fixed distance D apart. (A) Show that a converging lens of focal length F placed between the object and screen will form a real image on the screen for two positions that are separated by a distance d=(D(D-4F))^1/2 (B) Show that...
3. Deriving equations involving sin and cos

Homework Statement I'm asked to derive equation(2) from equation(1). equation(1): d=(tsin(2i))/((n^2-sin(i)^2)^1/2) equation(2): n=sin(i)(((2tcos(i/d))^2+1)^1/2) Homework Equations The Attempt at a Solution My attempts have got me nowhere, and I don't know how to even...
4. Finding the minimum angle of deviation for an equilateral prism

so i didn't cancel the 2's and i came up with: 1.5=((cos(60)sin(D)cos(D))/2)/(1/2) 1.5=((1/2sin(D)cos(D))/2)x2 0.75=(1/2sin(D)cos(D))/2 1.5=(1/2sin(D)cos(D)) 1.5=1/2(1/2(2sin(D)cos(D))) 3=1/2(1/2sin(2D)) 6=1/2sin(2D) 12=sin(2D) ?
5. Optics, involving index of refraction

I have a drawing that shows the viewing area from a point under the water going towards the surface at an unknown angle, then the viewing area widening once it breaks the surface. But I don't understand how to find the depth at which the viewing area is 180 degrees once it breaks the surface.
6. Finding the minimum angle of deviation for an equilateral prism

Homework Statement Use the formula: n=(sin(A+D)/2)/(sin(A)/2) to find D for an equilateral prism of index of refraction n=1.50 (where A=apex angle for a prism=60 degrees in this case, and D=minimum angle of deviation) Homework Equations Snell's Law: (n1)sin(i)=(n2)sin(r)...
7. Optics, involving index of refraction

Homework Statement At what distance below the surface of a lake will a fish have a 180 degree field view above the water surface (if the fish is looking up toward the surface of the lake) ? -Assume the index of refraction for water to be 1.33 and that of air to be 1.00 Homework...
8. Deriving equations involving sin and cos

Thanks, that was just the help I needed! Now I've been asked to derive a third equation from equation #2. equation #3: d=ti(n-1)/n , this equation approximates the displacement for small incident angles(i). (where i is measured in radians, n=index of refraction of the glass, note...
9. Deriving equations involving sin and cos

Homework Statement This problem deals with the displacement of a light ray as it travels through a glass medium. Starting with the equation #1: d=S[sin(i)cos(r)-cos(i)sin(r)] (where d=the length of displacement of the light ray in the glass medium, i=angle of incidence...
10. Isothermal expansion of an ideal gas

Homework Statement One mole of monatomic ideal gas is taken from an initial pressure(P) and volume(V) to a final pressure(2P) and volume(2V). It goes from pressure=P and volume=V to pressure=P/2 and volume=2V through isothermal expansion and from there volume stays constant but the pressure...