Physices Questions on mirror and refractions .. Help !!?

Question

Q1 an object 3cm in hight located 40 cm from a concave mirror with radius of curvature R = 50 cm.

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Q2 A convex mirror of focal length 25 cm if man stand about 20m from the mirror what the location of his image appear of he in mirror

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Q3 A concave mirror have a diameter 140 cm of sphere if there is a body reflacted 30 cm from the mirror find the distance of body from mirror.

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Q4 A ray of light travels from the air into water at angle with surface 60 ° , the index refraction of water 1.33

find :

A) the Angle of refraction.

B) the speed of light in water.

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Answer 1

Q1---What is the question? If you want the image distance

1/o +1/i =1/f

f= (1/2)R=25cm

1/25 =1/40 +1/i

1/i = 1/25 -1/40

1/i =0.04 -0.025 = 0.015

i = 67 cm

Q2---Use 1/o +1/i = 1/f

o is negative because you measure it left from the surface away from the light direction. i is negative because it is a virtual image.

1/(-20)  + 1/(-0.25) = 1/f

f = -0.25 meters = - 25 cm

f is negative because it is a convex mirror (diverging mirror)

Q3- D=140cm

R=70cm

f=35cm

1/o +1/i = 1/f

1/-o = 1/f -1/i = 1/35 - 1/30=0.0285714286 - 0.0333333333

1/-o =-0.0047619047

o =210 cm

Q4

n1sin30 =n2sinr

sinr =sin30/1.33 = .5/1.33 =0.37593985

r = arcsin(0.37593985) = 22 degrees

arcsin means the angle whose sine is...

v = c/n= c/1.33 = = 0.75c = 2.25 x 10^8 m/s

Answer 2

1. If you want to know the the distance of the image, use mirror formula  1/u + 1/v = 1/f   v= 66.66cm

2. Again use mirror formula 1/u --1/v = 1/f    v= 100cm

3.  The focal length is 35cm. The image is at 30cm from the mirror.  u= 210 cm   The image being very near to focal length, theoretically the object should be at infinity.

4. Sin i/Sin r  = 1.33   Angle of incidence is 30 deg with the normal.   Angle r = 22 Deg approx