I've tried to attempt the first part of the problem(spent over an hour on this) as second part could be easily optained with some calculus ,I asked my friend but alas nobody could conjure the solution to this dangerous trigonometric spell.
It was just pages and pages of concoction of...
I am extremely confused by the use of the term coefficient of increase of something. For example , if it is stated that the index of refraction varies linearly with a coefficient of 2.5×10^-5, how is this coefficient defined? Is it simply the slope of the line plotted with index of refraction on...
1. Homework Statement
Derive an analytic expression for the distance from the vertex to the focus for a particular ray in terms of (i) the radius of curvature R of the concave mirror (ii) the angle of incidence θ between incident ray and radius of the mirror. Hence show that the focus moves...
Is there a simple way to determine or prove this? Real images are always inverted, and unlike virtual images can be projected onto a screen (I'm not even sure what this means to be honest). If I look at the back end of a spoon (convex mirror), the image is always upright and therefore virtual...
1. Homework Statement
At the outside, there is a vertical stick with a length of 1.1 meter and its shadow on the surface of an earth is 1.3 meter, there also is light pole and its shadow length is 5.2 meters, what is the height of that light pole?
2. Homework Equations
Trigonometry equations...
The focal of the lens equivalent of two thin lens at distance h is
$$1/f=1/f_1+1/f_2+h/(f_1 f_2)$$
Therefore, supposing that ##f_1>0## and ##f_2>0## (both lenses are convergent), if ##f_1+f_2 <h## then the equivalent lens should be divergent.
Nevertheless consider the example in picture...
1. Homework Statement
Draw the ray diagram of the case of a diverging lens where both object and image are virtual, that is ##f<0## , ##p<0## with ##p<f##
2. Homework Equations
3. The Attempt at a Solution
I did not find this particular case of ray diagram in any textbook so I would...
1. Homework Statement
2. Homework Equations
We will call ##s## the distance of the object from the first lens, ##s'## the distance of the image from the first lens and ##s''## the distance of the image from the second lens.
The Gauss's lens equation:
$$\frac{1}{s}...
1. Homework Statement
A person's eye has a near point of 7 cm. The cornea at the outer surface of the eye has a refractive index of n_c = 1.376 and forms a convex shape with a radius of curvature of R_2 = 8 mm against air. The figure below shows the same eye with a contact lens (refractive...
A plane mirror forms a virtual image of a real object placed in front of it and a real image of a virtual object placed in front of it. I can't picture the second case. Please show me a ray diagram showing real image formation by a plane mirror or just explain the case of real image formation by...
1. Homework Statement
Hi!
I have lately come across some tricky experimental physics tasks, where no solution is given. Some of them involved parts where the focal lenght of a convex lens had to be measured with a laser. How do you do this?
2. Homework Equations
1/l + 1/d = 1/f (1)
where f...
I am trying to follow the derivation of lens maker's formula from the textbook "University Physics", p.1133 (https://books.google.com.hk/books?id=nQZyAgAAQBAJ&pg=PA1133#v=onepage&q&f=false [Broken])
I can understand the first equation because it is just the object–image relationship for...
1. Homework Statement
Given a "new type" of optical fiber (index of refraction n = 1.23), a laser beam is incident on the flat end of a straight fiber in air. Assume nair = 1.00. What is the maximum angle of incidence Ø1 if the beam is not to escape from the fiber? (See attached file for...
1.Problem: A vessel is quarter filled with a liquid of refractive index A. the remaining parts of the vessel is filled with an immiscible liquid of refractive index 3A/2. The apparent depth of the vessel is 50% of the actual depth. the value of A is?
1)1 2)3/2 3)2/3 4)4/3
Solution: 1...
Hi,
I am familiar with drawing rays through a lens. But when a few lenses are put together, things become confusing to me.
For example, if a first positive thin lens at 0 forms a real image 10cm away, what would happen when we put a second positive thin lens, say at 5cm along the optical...