# 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

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