Q. (a) Determine the'effective focal length' of the grouping of the two lenses in Exercise 9.10 if they are placed 8.0 cm a part with their principal axes coincident. Performed the answer depend on which side of the combination a beam of parallel light is incident? Is the idea of effective focal length of this system useful at all? (b)T he object 1.5 cm in size is placed on the side of the convex lens in the arrangement (a) above. The distance among the object and the convex lens is 40cm. Determine the exaggeration produced by the two < lens system and the size of the image.
Answer
A Focal length of the convex lens, f1=30cm
A Focal length of the concave lens, f2=-20cm
The Distance between the two lenses d=8.0cm
(a)While the parallel beam of light is incident on the convex lens first:
As-per to the lens formula we have
![2429_Determine the exaggeration produced by the two lens system.png](https://www.expertsmind.com/CMSImages/2429_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system.png)
Where
U1=Object distance=∞
v1=Image distance
v2=Image distance
![1528_Determine the exaggeration produced by the two lens system1.png](https://www.expertsmind.com/CMSImages/1528_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system1.png)
The image will perform as a real object for the convex lens.
Pertaining lens formula to the convex lens, we have:
![1753_Determine the exaggeration produced by the two lens system2.png](https://www.expertsmind.com/CMSImages/1753_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system2.png)
Where,
U1=Object distance
=- (20+d)=-(20+8)=-28cm
V1=Image distance
![2365_Determine the exaggeration produced by the two lens system3.png](https://www.expertsmind.com/CMSImages/2365_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system3.png)
Therefore the parallel incident beam appears to diverge from a point that is (420-4) 416 cm from the left of the centre of the combination of the two lenses.
The answer does depend on the side of the combination at which the parallel beam of light is incident. The notion of effectual focal length does not seem to be useful for this combination.
(b)Height of the image h 1=1.5cm
An Object distance from the side of the convex lens u1=-40cm
|u1|=40cm
As-per to the lens formula:
![1447_Determine the exaggeration produced by the two lens system4.png](https://www.expertsmind.com/CMSImages/1447_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system4.png)
Where v1=Image distance
![1017_Determine the exaggeration produced by the two lens system5.png](https://www.expertsmind.com/CMSImages/1017_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system5.png)
Magnification=120/40=3
Therefore the magnification due to the convex lensis3.
The image produced by the convex lens acts as an object for the concave lens .According to the lens formula:
![5_Determine the exaggeration produced by the two lens system6.png](https://www.expertsmind.com/CMSImages/5_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system6.png)
Where
U2=Object distance
=+ (120-8)=112cm.
V2 =Image distance
![1080_Determine the exaggeration produced by the two lens system7.png](https://www.expertsmind.com/CMSImages/1080_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system7.png)
Magnification ![1335_Determine the exaggeration produced by the two lens system8.png](https://www.expertsmind.com/CMSImages/1335_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system8.png)
= 2240/92 x 1/112 = 20/92
Therefore the magnification due to the concave lens is 20/92.
The magnification produced by the grouping of the two lenses is calculated as
m x m'
= 3 x 20/92 = 60/92 = 0.652
The magnification of the grouping is given as
![2113_Determine the exaggeration produced by the two lens system9.png](https://www.expertsmind.com/CMSImages/2113_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system9.png)
Where
h1= Object size=1.5cm
h2 = Size of the image
![194_Determine the exaggeration produced by the two lens system10.png](https://www.expertsmind.com/CMSImages/194_Determine%20the%20exaggeration%20produced%20by%20the%20two%20lens%20system10.png)
Therefore the height of the image is 0.98 cm.