Chapter 23 Optical instruments

Example 23.1 Page no 704

In [1]:
#Given
f=5.0                         #cm
D=25

#Calculation
M=1+(D/f)

#Result
print"Magnifying power is",M

Magnifying power is 6.0

Example 23.2 Page no 704

In [6]:
#Given
f=6.25                   #cm
v=-25

#Calculation
u=v*f/(v-f)
M=1+(D/f)
M1=D/f

#Result
print"(i) The distance of the object from the lens is", M
print"(ii) Anguar magnification is",M1

(i) The distance of the object from the lens is 5.0
(ii) Anguar magnification is 4.0

Example 23.3 Page no 704

In [15]:
#Given
u=-9
f=10                      #cm
v1=-25.0

#Calculation
v=u*f/(u+f)
M=v/u
u=-v1*f/(v1-f)
M1=1-(v1/f)

#Result
print"(i) Magnification is", M,"\n Size of each square in the image will appear as 100 mm**2"
print"(ii) Magnification is",M1

(i) Magnification is 10 
 Size of each square in the image will appear as 100 mm**2
(ii) Magnification is 3.5

Example 23.4 Page no 704

In [28]:
#Given
v=-25
f=10.0

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

#Result
print"(a) Distance is", round(u,2),"cm"
print"(b) Magnification is",m
print"(c) Magnification is",M

(a) Distance is 7.14 cm
(b) Magnification is 3.5
(c) Magnification is 3.5

Example 23.5 Page no 705

In [29]:
#Given
M=-30
fe=5                      #cm
D=25                     #cm

#Calculation
m0=M/(1+(D/fe))

#Result
print"Magnification produced is",m0

Magnification produced is -5

Example 23.6 Page no 705

In [34]:
#Given
f0=4
u0=-6
D=25
fe=6.0

#Calculation
v0=f0*u0/(f0+u0)
M=v0/u0*(1+(D/fe))

#Result
print"Magnification produceed by the microscope is", round(M,2)

Magnification produceed by the microscope is -10.33

Example 23.7 Page no 705

In [41]:
#Given
L=20
fe=5
f0=1.0                   

#Calculation
v01=L-fe
u0=v01*f0/(f0-v01)
M=v01*D/(u0*fe)

#Result
print"Magnification power is", M,"\nThe -ve sigh shows that the image formed is inverted and real"

Magnification power is -70.0 
The -ve sigh shows that the image formed is inverted and real

Example 23.8 Page no 705

In [46]:
#Given
f=36                         #cm
M=-8

#Calculation
fe=-f/(M-1)
f0=-M*fe

#Result
print"Focal length of the lenses is", fe,"cm and",f0,"cm"

Focal length of the lenses is 4 cm and 32 cm

Example 23.9 Page no 705

In [49]:
#Given
f=75                  #cm
fe=5.0
D=25 

#Calculation
M=-f/fe*(1+(fe/D))

#Result
print"Magnying power is",M

Magnying power is -18.0

Example 23.10 Page no 705

In [54]:
#Given
f0=140
fe=5
D=25.0

#Calculation
M=-f0/fe
M1=-(f0/fe)*(1+(fe/D))

#Result
print"(a) Magnefying power, when telescope is in normal adjustment is", M
print"(b) Magnifying power, when image is formed at least distance of distinct vision is is",M1

(a) Magnefying power, when telescope is in normal adjustment is -28
(b) Magnifying power, when image is formed at least distance of distinct vision is is -33.6

Example 23.11 Page no 706

In [71]:
#Given
f0=1                        #m
fe=0.05
I=0.92*10**-2
u0=38*10**-7
fe1=5.0                        #cm
ve=-25

#Calculation
d=I*u0/f0
L=f0+fe
ue=ve*fe1/(fe1-ve)
L1=(f0*10**2)-ue

#Result
print"(i) Distance between two lenses is", L*10**2,"cm"
print"(ii) Distance when final image at 25 cm from the eye is",round(L1,2),"cm"

(i) Distance between two lenses is 105.0 cm
(ii) Distance when final image at 25 cm from the eye is 104.17 cm

Example 23.12 Page no 706

In [74]:
#Given
M=-20
R=120

#Calculation
f0=R/2.0
fe=-f0/M

#Result
print"Focal length of the eye piece is",fe,"cm"

Focal length of the eye piece is 3.0 cm

Example 23.13 Page no 706

In [76]:
#Given
d=0.8                        #cm
D=508

#Calculation
B=D**2/d**2

#Result
print"The telescope can see a star ",B,"time sfarther than the faintest star that can be seen with naked eye."

The telescope can see a star  403225.0 time sfarther than the faintest star that can be seen with naked eye.

Example 23.14 Page no 706

In [87]:
#Given
ve=-25                      #cm
fe=6.25
a=15
f0=2

#Calculation
ue=-ve*fe/(ve-fe)
v0=a+ue
u0=f0*v0/(f0-v0)
v01=a-fe
u01=v01*f0/(f0-v01)

#Result
print"(a) Distance when final image at least distance of distinct vision is", u0,"cm"
print"(b) Distance when final image is at infinity is",round(u01,2),"cm"

(a) Distance when final image at least distance of distinct vision is -2.5 cm
(b) Distance when final image is at infinity is -2.59 cm

Example 23.15 Page no 707

In [95]:
#Given
a=10
D=24
fe=20.0

#Calculation
import math
A=a/(1+(D/fe))/100.0

#Result
print"Angle is", round(A,4),"radian"

Angle is 0.0455 radian

Example 23.16 Page no 707

In [103]:
#Given
f0=-0.5                          #m
fe=0.01
d=3.48*10**6
r=3.8*10**8
a1=15

#Calculation
M=f0/fe
a=d/r
I=a*a1

#Result
print"(a) Angular Magnification of the telescope is",M
print"(b) Diameter of the image is", round(I,3),"m"

(a) Angular Magnification of the telescope is -50.0
(b) Diameter of the image is 0.137 m