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'
```

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
```

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
```

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
```

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
```

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)
```

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
```

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
```

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
```

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
```

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
```

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))
```

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)
```