A fish is at a depth d in water of refractive index 4/3. If a transparent slab of refractive index 3/2 and thickness d/2 is placed on the surface of water, then which one of the following is the apparent depth of the fish as observed by an observer in air?
\(13d/12\)
For nearly normal viewing through a stack of transparent layers, the total apparent depth measured from the topmost surface equals the sum of each layer's real thickness divided by its own refractive index. Here water has real depth d and refractive index \(4/3\), and the slab has thickness \(d/2\) and refractive index \(3/2\). So apparent depth \(= \dfrac{d}{4/3} + \dfrac{d/2}{3/2} = \dfrac{3d}{4} + \dfrac{d}{3} = \dfrac{9d+4d}{12} = \dfrac{13d}{12}\). Hence the apparent depth of the fish is \(13d/12\).
Similar Questions
A rainbow is produced due to which one of the following phenomenon?
Consider the following statements about a microscope and a telescope:
1. Both the eyepiece and the objective of a microscope are convex lenses.
2. The focal length of the objective of a telescope is larger than the focal length of its eyepiece.
3. The magnification of a telescope increases with the increase in focal length of its objective.
4. The magnification of a microscope increases with the increase in focal length of its objective.
Which of the statements given above are correct?The refractive index of crown glass is close to 3/2. If the speed of light in air is c, then the speed of light in the crown glass will be close to
Which of the following statements regarding lenses is not correct?
Light rays move in straight lines. But through an optical fibre, they can move in any type of zigzag path because
Two convex lenses with power 2 diopter are kept in contact with each other. The focal length of the combined lens system is
The mirror used as rear-view mirrors in vehicle are
Concave mirrors are used in headlights of vehicles, because they
Which one of the following statements is not correct?
Which one of the following statement is correct about the magnification of an optical microscope?
Important Questions from Refraction and Reflection
A convex lens of focal length f will form a magnified real image of an object, if the object is placed.
A ray of light travelling in the direction \(\frac{1}{2} (\hat i + \sqrt 3 \hat j)\) is incident on a plane mirror. After reflection it travels along the direction \(\frac{1}{2} (\hat i - \sqrt 3 \hat j)\) The angle of incidence is:
Twinkling of stars is due to atmospheric
An optical fibre has a core material of refractive index of 1.55 and cladding material of refractive index of 1.50. The numerical aperture of the fibre is
- The refracting angle of a prism is $A$. The refractive index of the material of the prism is $\frac{1+\cos A}{\sin A}$. The angle of minimum deviation is:
