Ray Optics and Optical Instruments Test 5

When the lens is in air, we have (from lens maker's equation), 1/20 = [(1.5/1) - 1) (1/R1- 1/R2). 
We are not bothered about the signs of R1 and R2 since they are unknown quantities. 
Even though we know that the convergent lens will become divergent in the denser medium, we write the lens maker's equation without bothering about the sign of its unknown focal length in the liquid. If if is the focal length in the liquid, we can write, 
1/f = ((1.5/1.6) - 1) (1/R1 - 1/R2). 
Dividing the first equation by the second, we obtain f/20 = 0.5x1.6/(-0.1) from which f = -160 cm

Using the lens maker’s formula we get
p= (μ−1) (1/R₁​+1/R₂​)
As we can clearly see, when R₁= R₂= 5cm then the maximum power is achieved.

Consider refraction of light from infinity at first surface,
(μ2/v)​​−( μ1/u​)​=(μ2​−μ1/R)​​
(1.5​/ v1​)-(1.75/−∞)​=1.5−1.75​/−R
Consider refraction of this image from second surface,
​(1.75​/ v2)−(​1.5/v1)​=(1.75−1.5​)/R
Hence, v2​=3.5R
This is the image of light coming from infinity, therefore the focal length.
It is converging since focal length is positive.
 

M=−ϑ /u ​=−m/1​
ϑ=−mu
(1/ϑ​)−(1/u)​=1/f
1/mu​+1/u​=−1/f​
(1+m)​/xu=−1/f​
u= (1+m)​f/(m)

1/f= ((μ₂- μ₁)/ μ₁){(1/R₁) –(1/R₂)}
Refractive index of glass, μ₂=1.6, refractive index of liquid, μ₁=1.63
R₁=15 cm ,R₂=-15 cm
The focal length of this lens when immersed in a fluid is:
1/f=((1.6-1.63)/1.63){(1/15)-(1/-15)}
F=-416.67cm

A dioptre (British spelling) or dioptre (American spelling) is a unit of measurement of the optical power of a lens or curved mirror, which is equal to the reciprocal of the focal length measured in metres. (1 dioptre = 1 m−1.) It is thus a unit of reciprocal length.