CHAPTER19 : OPTICAL INSTRUMENTS

Example E1 : Pg 420

In [1]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.1
# determining which boy appears taller 

# given data
d1=4.# distance(in m) of boy1 from the eye
d2=5.# distance(in m) of boy2 from the eye
h1=52.# height(in inch) of boy1
h2=55.# height(in inch) of boy2

# calculation
alpha1=h1/d1# angle subtended by the first boy on the eye
alpha2=h2/d2# angle subtended by the second boy on the eye
if(alpha1>alpha2) :
    print'the first boy will look taller to the eye'
if(alpha1<alpha2) :
    print'the second boy will look taller to the eye'
else :
    print'Both boys will appear same in height to the eye'

the first boy will look taller to the eye
Both boys will appear same in height to the eye

Example E2 : Pg 422

In [2]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.2
# calculation of the angular magnification and the length of the microscope tube

# given data
fo=1.*10.**-2.# focal length(in m) of the objective lens
fe=2.5*10.**-2.# focal length(in m) of the eyepiece
u=-1.2*10.**-2.# object distance(in m)
D=25.*10.**-2.# least distance(in m) for the clear vision

# calculation
v=1./((1./fo)+(1./u))# distance where the first image is formed ....by the lens formula
m=(v*D)/(u*fe)# angular magnification
L=v+fe# length of the tube

print'the angular magnification is ',round(m)
print'\nthe length of the microscope tube is cm',L*10**2

the angular magnification is  -50.0

the length of the microscope tube is cm 8.5

Example E3 : Pg 426

In [3]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.3
# calculation of the power of lens for the spectacles

# given data
d=1.5# distance(in m) upto which the man can clearly see objects 

# calculation
f=-d# focal length of the lens
P=1./f# definition of power of the lens

print'the power of lens for the spectacles is D',P

the power of lens for the spectacles is D -0.666666666667

WORKED EXAMPLES

Example E1w : Pg 427

In [4]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.1w
# calculation of the angular magnification 

# given data
f=12.*10.**-2.# focal length(in m) of the simple microscope
D=25.*10.**-2.# distance(in m) at which the image is formed away from the eye

# calculation
m=1.+(D/f)# angular magnification

print'the angular magnification is %3.2f',m

the angular magnification is %3.2f 3.08333333333

Example E2w : Pg 427

In [5]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.2w
# calculation of the object distance to obtain maximum angular magnification for a normal eye

# given data
D=10.# power(in D) of the lens
v=-25.*10.**-2.# image distance(in m) i.e at the near point

# calculation
f=1./D# focal length
u=1./((1./v)-(1./f))# lens formula

print'the object distance to obtain maximum angular magnification for a normal eye is cm',u*10**2

the object distance to obtain maximum angular magnification for a normal eye is cm -7.14285714286

Example E3w : Pg 428

In [6]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.3w
# calculation of the position of the image ,linear magnification and the angular magnification

# given data
u=-3.6*10.**-2.# object distance(in m) 
f=4.*10.**-2.# focal length(in m)
D=25.*10.**-2.# least distance for clear vision

# calculation
v=1./((1./f)+(1./u))# lens formula
m=v/u# linear magnification
alpha=D/abs(u)# angular magnification

print'the image distance is cm',v*10**2
print'the linear magnification is',m
print'the angular magnification is',round(alpha)

the image distance is cm -36.0
the linear magnification is 10.0
the angular magnification is 7.0

Example E4w : Pg 428

In [7]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.4w
# calculation of the object distance and the angular magnification

# given data
fo=1.*10.**-2.# focal length(in m) of the objective lens
fe=5.*10.**-2.# focal length(in m) of the eyepiece
d=12.2*10.**-2.# separation(in m) between the objective lens and the eyepiece
D=25.*10.**-2.# least distance(in m) for the clear visio

# calculation
ve=-D# image distance for the eyepiece
ue=1./((1./ve)-(1./fe))# object distance for eyepiece....by the lens formula
vo=d-abs(ue)# image distance for objective lens
uo=1./((1./vo)-(1./fo))# object distance for objective lens....by the lens formula
m=(vo/uo)*(1.+(D/fe))# angular magnification

print'the object should be placed at a distance of cm from the objective lens to focus it properly',abs(uo*10**2)
print'the angular magnification is ',m

the object should be placed at a distance of cm from the objective lens to focus it properly 1.14218009479
the angular magnification is  -42.2

Example E5w :Pg 428

In [8]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.5w
# calculation of the object distance and the angular magnification for the least strain in the eyes

# given data
fo=.5*10.**-2.# focal length(in m) of the objective lens
fe=5*10.**-2.# focal length(in m) of the eyepiece
d=7*10.**-2.# separation(in m) between the objective lens and the eyepiece
D=25*10.**-2.# least distance(in m) for the clear vision

# calculation
v=d-fe# distance at which the first image should be formed
u=1./((1./v)-(1./fo))# lens formula for the objective lens
m=(v*D)/(u*fe)# angular magnification

print'the object distance for the least strain in the eyes is cm',abs(u*10**2)
print'the angular magnification for the least strain in the eyes is',m

the object distance for the least strain in the eyes is cm 0.666666666667
the angular magnification for the least strain in the eyes is -15.0

Example E6w : Pg 429

In [9]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.6w
# calculation of the length of the tube and the angular magnification produced by the telescope

# given data
fo=200.*10.**-2.# focal length(in m) of the objective lens
fe=4.*10.**-2.# focal length(in m) of the eyepiece
u=10.*10.**3.# object distance(in m)

# calculation
L=fo+fe# length of the tube
m=-fo/fe# angular magnification

print'the length of the tube is cm',L*10**2
print'the angular magnification is',m

the length of the tube is cm 204.0
the angular magnification is -50.0

Example E7w : Pg 429

In [10]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.7w
# calculation of the tube length,magnifying power and angular magnification

# given data
fo=50.*10.**-2.# focal length(in m) of the objective lens
fe=-5.*10.**-2.# focal length(in m) of the eyepiece
u=-2.# object distance(in m)

# calculation
L=fo-abs(fe)# length of the tube
m=-fo/fe# magnifying power
v=1./((1./fo)+(1./u))# by lens formula for the objective lens
Ldash=v-abs(fe)# tube length
mdash=v/abs(fe)# angular magnification

print'the tube length for large distance viewing is cm',L*10**2
print'the magnifying power for the large distance viewing is',m
print'the tube length for viewing object at 2 m is cm',Ldash*10**2
print'the angular magnification for viewing object at 2 m is',mdash

the tube length for large distance viewing is cm 45.0
the magnifying power for the large distance viewing is 10.0
the tube length for viewing object at 2 m is cm 61.6666666667
the angular magnification for viewing object at 2 m is 13.3333333333

Example E8w : Pg 429

In [11]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.8w
# calculation of the angular magnification due to the converging lens

# given data
f=50.*10.**-2.# focal length(in m) of the converging lens
d=25.*10.**-2.# distance(in m) from where the image can be seen by unaided eye

# calculation
# linear size = f*alpha
# angle formed .....abs(beta) = f*abs(alpha)/d
m=-f/d# angular magnification...m = -abs(beta)/abs(alpha)

print'the angular magnification due to the converging lens is',m

the angular magnification due to the converging lens is -2.0

Example E9w : Pg 429

In [12]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.9w
# calculation of the power of lens and maximum distance that can be seen clearly

# given data
u=-25.*10.**-2.# object distance(in m)
v=-40.*10.**-2.# image distance(in m)....i.e equal to near point distance
vdash=-250.*10.**-2.# maximum distance(in m) that an unaided eye can see....i.e equal to far point distance

# calculation
f=1./((1./v)-(1./u))# focal length ....by using the lens formula
P=1./f# power of the lens
d=1./((1./vdash)-(1./f))# maximum distance for clear vision.... by using the lens formula

print'the power of the lens is D',P
print'the maximum distance upto which,the person will be able to see clearly is %d cm',round(abs(d*10**2))

the power of the lens is D 1.5
the maximum distance upto which,the person will be able to see clearly is %d cm 53.0

Example E10w : Pg 430

In [13]:
# developed in windows XP operating system 32bit
# platform Scilab 5.4.1
#clc;clear;
# example 19.10w
# calculation of the near point and the distance of the retina from the lens 

# given data
P1=50.# power1(in D) of the lens
P2=60.# power2(in D) of the lens

# calculation
# for the eye in fully relaxed condition,the focal length is the largest.
# larger the focal length,smaller is the power of lens
if(P1<P2) :
    P=P1
else :
    P=P2
f=1./P# distance of the retina from lens ,equal to the focal length
# for eye focused at near point the power is maximum
if(P1>P2) :
    Pdash=P1
else :
    Pdash=P2
fdash=1./Pdash# focal length
v=abs(f)# image is formed at the retina
u=1./((1./v)-(1./fdash))# near point......using the lens formula

print'the distance of the retina from the lens is cm',f*10**2
print'the near point is at cm',abs(u*10**2)

the distance of the retina from the lens is cm 2.0
the near point is at cm 10.0