An unsymmetrical double convex thin lens forms the image of a point object on its axis. Will the position of the image change if the lens is reversed?
Download our app for free and get started
Key concept: Thin lens formula: $\frac{1}{\text{v}}-\frac{1}{\text{u}}=\frac{1}{\text{f}}$ For a given object position if focal length of the lens deos not change, the image posrition remains unchanged.
By lens maker's formula, $\frac{1}{\text{f}}=(\mu-1)\Big(\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}\Big)$ For this position $R_1$ is positive and $R_2$ is negative.
Hence focal lenght at this position $\frac{1}{\text{f}_1}=(\mu-1)\Big(\frac{1}{(+\text{R}_1)}-\frac{1}{(-\text{R}_2)}\Big)=(\mu-1)\Big(\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}\Big)$
Now the lens is reversed,
At this position, $R_2$ is positive and $R_1$ is negative. Hence focal length at this position is $\frac{1}{\text{f}_2}=(\mu-1)\Big(\frac{1}{(+\text{R}_2)}-\frac{1}{(-\text{R}_1)}\Big)=(\mu-1)\Big(\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}\Big)$ We can observe the focal length of the lens does not change in both positions, hence the image position remains unchanged.
By lens maker's formula, $\frac{1}{\text{f}}=(\mu-1)\Big(\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}\Big)$ For this position $R_1$ is positive and $R_2$ is negative.
Hence focal lenght at this position $\frac{1}{\text{f}_1}=(\mu-1)\Big(\frac{1}{(+\text{R}_1)}-\frac{1}{(-\text{R}_2)}\Big)=(\mu-1)\Big(\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}\Big)$
Now the lens is reversed,
At this position, $R_2$ is positive and $R_1$ is negative. Hence focal length at this position is $\frac{1}{\text{f}_2}=(\mu-1)\Big(\frac{1}{(+\text{R}_2)}-\frac{1}{(-\text{R}_1)}\Big)=(\mu-1)\Big(\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}\Big)$ We can observe the focal length of the lens does not change in both positions, hence the image position remains unchanged.
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionA gun of mass M fires a bullet of mass m with a horizontal speed V. The gun is fitted with a concave mirror of focal length f facing tpwards the receding bullet. Find the speed of separation of the bullet and the image just after the gun was fired.
- 2View SolutionA normal eye has retina 2cm behind the eye-lens. What is the power of the eye-lens when the eye is
- Fully relaxed,
- Most strained?
- 3Light is incident from glass $(\mu=1.50)$ to water $(\mu=1.33).$ Find the range of the angle of deviation for which there are two angles of incidence.View Solution
- 4View Solution
- State Huygen’s principle. Using this principle draw a diagram to show how a plane wave front incident at the interface of the two media gets refracted when it propagates from a rarer to a denser medium. Hence verifiy Snell’s law of refraction.
- When monochromatic light travels from a rarer to a denser medium, explain the following, giving reasons:
- Is the frequency of reflected and refracted light same as the frequency of incident light?
- Does the decrease in speed imply a reduction in the energy carried by light wave?
- 5View SolutionWill the focal length of a lens for red light be more, same or less than that for blue light?
- 6View SolutionA converging lens of focal length 15cm and a converging mirror of focal length 10cm are placed 50cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40cm from the lens. Find the locations of the two images formed.
- 7A biconvex thick lens is constructed with glass $(\mu=1.50)$ Each of the surfaces has a radius of 10cm and the thickness at the middle is 5cm. Locate the image of an object placed far away from the lens.View Solution
- 8View Solution
- A point object is placed on the principal axis of a convex spherical surface of radius of curvature R, which separates the two media of refractive indices $n_1$ and $n_2(n_2 > n_1)$. Draw the ray diagram and deduce the relation between the object distance (u), image distance (v) and the radius of curvature (R) for refraction to take place at the convex spherical surface from rarer to denser medium.
- A converging lens has a focal length of 20 cm in air. It is made of a material of refractive index 1.6. If it is immersed in a liquid of refractive index 1.3, find its new focal length.
- 9View SolutionAt what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.
- 10The convex surface of a thin concavo-convex lens of glass of refractive index 1.5 has a radius of curvature 20cm. The concave surface has a radius of curvature 60cm. The convex side is silvered and placed on a horizontal surface as shown in figure.View Solution
- Where should a pin be placed on the axis so that its image is formed at the same place?
- If the concave part is filled with water $\Big(\mu=\frac{4}{3}\Big),$ find the distance through which the pin should be moved so that the image of the pin again coincides with the pin.
