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