# Chapter 17 Refraction of the light¶

## Example 17.1 Page no 918¶

In [7]:
#Given
u1=1.50
u2=1.33

#Calculation
import math
sinr=u1*math.sin(50*3.14/180.0)/u2
a=math.asin(sinr)*180/3.14

#Result
print"Angle of refraction is", round(a,1),"degree"

Angle of refraction is 59.8 degree


## Example 17.2 Page no 918¶

In [13]:
#Given
u1=1.0
u2=1.526
i=45                      #degree
#Calculation
sinr=(u1*math.sin(i*3.14/180.0))/u2
r=math.asin(sinr)*180/3.14
d=i-r

#Result
print"Angle of deviation is", round(d,2),"degree"

Angle of deviation is 17.39 degree


## Example 17.3 Page no 918¶

In [22]:
#Given
c=3.0*10**8
u=1.5
f=6*10**14                      #Hz

#Calculation
v=c/u
l=c/f
lm=v/f

#Result
print"(i) Wavelength of light in air is", l,"m"
print"(ii) Wavelength of light in glass is",round(lm*10**7,1)*10**-7,"m"

(i) Wavelength of light in air is 5e-07 m
(ii) Wavelength of light in glass is 3.3e-07 m


## Example 17.4 Page no 919¶

In [26]:
#Given
ug=1.5
uw=1.3
vw=2.25*10**8

#Calculation
vg=(uw*vw)/ug

#Result
print"Speed of the light in glass is", vg*10**-8,"*10**8 m/s"

Speed of the light in glass is 1.95 *10**8 m/s


## Example 17.5 Page no 919¶

In [39]:
#Given
u=1.6
t=8
t1=4.5
u1=1.5
t2=6
u2=1.33

#Calculation
d=t*(1-(1/u))
d1=t1*(1-(1/u1))
d2=t2*(1-(1/u2))
D=d+d1+d2

#Result
print"Position of mark from the bottom is", round(D,0),"cm"

Position of mark from the bottom is 6.0 cm


## Example 17.6 Page no 919¶

In [49]:
#Given
uw=1.33
uo=1.20

#Calculation
import math
uow=uw/uo
sinr=(math.sin(30*3.14/180.0))/uow
r=math.asin(sinr)*180/3.14

#Result
print"Angle of refraction in water is", round(r,1),"degree"

Angle of refraction in water is 26.8 degree


## Example 17.7 Page no 920¶

In [54]:
#Given
v=2.0*10**8                           #m/s
c=3*10**8                           #m/s
d=6.0                               #cm

#Calculation
ug=c/v
a=d/ug
D=d-a

#Result
print"Distance through which ink dot appears to be raised is", D,"cm"

Distance through which ink dot appears to be raised is 2.0 cm


## Example 17.8 Page no 924¶

In [60]:
#Given
ug=1.5
uw=1.33

#Calculation
u1=ug/uw
sinC=1/u1
C=math.asin(sinC)*180/3.14

#Result
print"Critical angle is", round(C,2),"degree"

Critical angle is 62.49 degree


## Example 17.9 Page no 924¶

In [65]:
#Given
v=1.5*10**8
c=3.0*10**8

#Calculation
import math
a=v/c
C=math.asin(a)*180/3.14

#Result
print"Value of critical angle is", round(C,0),"Degree"

Value of critical angle is 30.0 Degree


## Example 17.10 Page no 924¶

In [74]:
#Given
uw=1.33

#Calculation
a=1/uw
b=math.sin(a)*180/3.14

#Result
print"Angle of refraction is", round(b,0),"degree"

Angle of refraction is 39.0 degree


## Example 17.11 Page no 924¶

In [79]:
#Given
a=4
b=6.0

#Calculation
import math
A=a/b
B=math.atan(A)*180/3.14
ur=1/(math.sin(B*3.14/180.0))

#Result
print"Refrective index of the liquid is", round(ur,1)

Refrective index of the liquid is 1.8


## Example 17.12 Page no 925¶

In [88]:
#Given
a=52                                   #Degree
b=33                                    #Degree

#Calculation
import math
u2=(math.sin(a*3.14/180.0))/(math.sin(b*3.14/180.0))
C=1/u2
A=math.asin(C)*180/3.14

#Result
print"Angle of refrection is", round(A,1),"Degree"

Angle of refrection is 43.7 Degree


## Example 17.13 Page no 932¶

In [94]:
#Given
u=-240.0
R=15.0                    #cm
u1=1.33
u2=1.5

#Calculation
v=1/((((u2-u1)/R)+(u1/u))/u2)

#Result
print"Position of the image is", round(v,0),"cm"

Position of the image is 259.0 cm


## Example 17.14 Page no 932¶

In [7]:
#Given
u=-9.0                        #cm
y=1
y1=1.5
R=-15.0                      #cm

#Calculation
v=1/(((y-y1)/R)-(y1/-u))

#Result
print"The value of distance is",v,"cm"

The value of distance is -7.5 cm


## Example 17.15 Page no 933¶

In [9]:
#Given
u=-15               #cm
y1=1
y2=1.5
R=-7.5              #cm

#Calculation
v=1/(((y1-y2)/R)-(y2/-u))

#Result
print"Position of the image is",v,"cm"

Position of the image is -30.0 cm


## Example 17.16 Page no 933¶

In [21]:
#Given
u=-60.0                    #cm
R=25.0                     #cm
y1=1
y2=1.5

#Calcution
v=1/((((y2-y1)/R)+(y1/u))/y2)
P=(y2-y1)/(R*10**-2)

#Result
print"Position of the image is", v,"cm"
print"Power of the refracting surface is", P,"dioptre"

Position of the image is 450.0 cm
Power of the refracting surface is 2.0 dioptre


## Example 17.17 Page no 934¶

In [24]:
#Given
u1=1
u2=1.5
R=1

#Calculation
x=(u1+u2)/(u2-u1)

#Result
print"Distance of the object is", x,"R"

Distance of the object is 5.0 R


## Example 17.18 Page no 934¶

In [30]:
#Given
R=7.5                            #cm
u1=1
u2=1.33

#Calculation
v=1/(((u1-u2)/R))

#Result
print"It gets focused at", round(v,1),"cm"

It gets focused at -22.7 cm


## Example 17.19 Page no 935¶

In [34]:
#Given
u1=1
u2=1.5
u=-10
v=-40                        #cm

#Calculation
R=-v*(u2-u1)/(u1+u2)

#Result
print"Curvature given to the bounding surface is", R,"cm (Convex)"

Curvature given to the bounding surface is 8.0 cm (Convex)


## Example 17.20 Page no 935¶

In [41]:
#Given
u1=1
u2=1.5
v=100                        #cm
R=20.0                        #cm
a=3
b=200.0

#Calculation
u1=(u2-u1)/R
u2=-1/(u1-(a/b))
d=-u2+R

#Result
print"The object distance from the centre of curvature is", d,"cm"

The object distance from the centre of curvature is 120.0 cm


## Example 17.21 Page no 952¶

In [50]:
#Given
ug=1.5
R1=50.0                     #cm
R2=-50.0                   #cm
uw=9/8.0

#Calculation
f=1/((ug-1)*((1/R1)+(1/R1)))
f1=1/((uw-1)*((1/R1)+(1/R1)))

#Result
print"(i) Focal length in air is", f,"cm"
print"(ii) Focal lenth in water is", f1

(i) Focal length in air is 50.0 cm
(ii) Focal lenth in water is 200.0


## Example 17.22 Page no 953¶

In [54]:
#Given
fa=20                          #cm
ug=9/8.0
uw=3/2.0

#Calculation
a=(uw-1)/(ug-1)
fw=a*fa
f=fw-fa

#Result
print"Change in focal length is", f,"cm"

Change in focal length is 60.0 cm


## Example 17.23 Page no 953¶

In [63]:
#Given
u=1.56
R1=20.0                      #cm
u1=-10.0                      #cm

#Calculation
f=1/((u-1)*(2/R1))
v=1/((1/u1)+(1/f))

#Result
print"Position of the image formed is", round(v,2)

Position of the image formed is -22.73


## Example 17.24 Page no 953¶

In [65]:
#Given
u=1.47

#Calculation
u1=u

#Result
print"The liquid is not water because refractive index of water is 1.33"

The liquid is not water because refractive index of water is 1.33


## Example 17.25 Page no 954¶

In [68]:
#Given
f=18                         #cm
u=1.5

#Calculation
R=(u-1)*f

#Result
print"Radius of the curvature is", R,"cm"

Radius of the curvature is 9.0 cm


## Example 17.26 Page no 954¶

In [78]:
#Given
u=-25.0                      #cm
f=10.0                       #cm
h1=5

#Calculation
v=1/((1/f)+(1/u))
h2=(v*h1)/u

#Result
print"Position of the image is", round(v,2),"cm"
print"Size of the image is",round(h2,2),"cm"

Position of the image is 16.67 cm
Size of the image is -3.33 cm


## Example 17.27 Page no 954¶

In [81]:
#Given
f=-15.0                     #cm
v=-10.0                       #cm

#Calculation
u=1/((1/v)-1/f)

#Result
print"The object is placed at a distance of", u,"cm"

The object is placed at a distance of -30.0 cm


## Example 17.28 Page no 954¶

In [85]:
#Given
v=-20.0                         #cm
u=-60.0                         #cm

#Calculation
f=1/((1/v)-(1/u))

#Result
print"Focal length of the lens is", f,"cm"
print"The lens is diverging"

Focal length of the lens is -30.0 cm
The lens is diverging


## Example 17.29 Page no 955¶

In [94]:
#Given
u=-10.0                       #cm
m=-3.0

#Calculation
v=m*u
f=1/((1/v)-(1/u))

#Result
print"Image formed at",v,"cm"
print"Focal length is",f,"cm"

Image formed at 30.0 cm
Focal length is 7.5 cm


## Example 17.30 Page no 955¶

In [102]:
#Given
P1=6
P2=-2.0

#Calculation
P=P1+P2
f=1/P

#Result
print"Focal length of the combination is", f*10**2,"cm"
print"Power of the combinationis",P,"D"

Focal length of the combination is 25.0 cm
Power of the combinationis 4.0 D


## Example 17.31 Page no 955¶

In [107]:
#Given
f1=20.0              #cm
f2=-40.0                #cm

#Calculation
f=1/((1/f1)+(1/f2))
P=1/f

#Result
print"Focal length is", f,"cm"
print"Power is",P*10**2,"D"

Focal length is 40.0 cm
Power is 2.5 D


## Example 17.32 Page no 955¶

In [109]:
#Given
a=2.0
b=1

#Calculation
u=(b/a)+b

#Result
print"Refractive index of the material is", u

Refractive index of the material is 1.5


## Example 17.33 Page no 955¶

In [113]:
#Given
f=-0.2                        #m
v=0.3                         #m

#Calculation
u=1/((1/v)-(1/f))

#Result
print"Position of the point is", u,"m"

Position of the point is 0.12 m


## Example 17.35 Page no 957¶

In [127]:
#Given
u1=-30.0                      #cm
f1=10.0
u2=10
f2=-10.0

#calculation
v1=1/((1/u1)+(1/f1))
v2=1/((1/u2)+(1/f2))
v3=-u1

#Result
print"Position of the image for first lens is", v1,"cm"
print"Position of the image for second lens is", round(v2*10**-2,0),"cm"
print"Position of the image for third lens is", v3,"cm"

Position of the image for first lens is 15.0 cm
Position of the image for second lens is -0.0 cm
Position of the image for third lens is 30.0 cm