Download App
Two convex lenses, each of focal length 10cm, are placed at a separation of 15cm with their principal axes coinciding,
  1. Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system.
  2. Find the location of the virtual image formed by the lens system of an object placed far away.
  3. Find the focal length of the equivalent lens.
(Note that the sign of the focal length is positive although the lens system actually diverges a parallel beam incident on it).
Download our app for free and get startedPlay store
  1. The beam will diverge after coming out of the two convex lens system because, the image formed by the first lens lies within the focal length of the second lens.
  2. For $1^{st}$ convex lens, $\frac{1}{\text{v}}-\frac{1}{\text{u}}=\frac{1}{\text{f}}\Rightarrow\frac{1}{\text{v}}=\frac{1}{10} \ (\text{since, u}=-\infty)$
or, $\text{v}=10\text{cm}$
for $2^{nd}$ convex lens, $\frac{1}{\text{v}'}=\frac{1}{\text{f}}+\frac{1}{\text{u}}$
or, $\frac{1}{\text{v}'}=\frac{1}{10}+\frac{1}{-(15-10)}=\frac{-1}{10}$
or, $\text{v}'=-10\text{cm}$
So, the virtual image will be at 5cm from $1^{st}$ convex lens.
  1. If, F be the focal length of equivalent lens,
Then, $\frac{1}{\text{F}}=\frac{1}{\text{f}_1}+\frac{1}{\text{f}_2}-\frac{\text{d}}{\text{f}_1\text{f}_2}\Rightarrow\frac{1}{10}+\frac{1}{10}-\frac{15}{100}=\frac{1}{20}$
$\Rightarrow\text{F}=20\text{cm}.$
art

Download our app
and 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.*
Download App

Similar Questions

  • 1
    A small block of mass m and a concave mirror of radius R fitted with a stand lie on a smooth horizontal table with a separation d between them. The mirror together with its stand has a mass m. The block is pushed at t = 0 towards the mirror so that it starts moving towards the mirror at a constant speed V and collides with it. The collision is perfectly elastic. Find the velocity of the image:
    1. At a time $\text{t}<\frac{\text{d}}{\text{V}}$
    2. At a time $\text{t}>\frac{\text{d}}{\text{V}}.$
    View Solution
  • 2
    1. 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.
    2. When monochromatic light travels from a rarer to a denser medium, explain the following, giving reasons:
      1. Is the frequency of reflected and refracted light same as the frequency of incident light?
      2. Does the decrease in speed imply a reduction in the energy carried by light wave?
    View Solution
  • 3
    Find the maximum magnifying power of a compound Microscope having a 25 diopter lens as the objective, a 5 diopter lens as the eyepiece and the separation 30cm between the two lenses. The least distance for clear vision is 25cm.
    View Solution
  • 4
    A pin of length 2.00cm is placed perpendicular to the principal axis of a converging lens. An inverted image of size 1.00cm is formed at a distance of 40.0cm from the pin. Find the focal length of the lens and its distance from the pin.
    View Solution
  • 5
    A particle is moving at a constant speed V from a large distance towards a concave mirror of radius R along its principal axis. Find the speed of the image formed by the mirror as a function of the distance x of the particle from the mirror.
    View Solution
  • 6
    1. Derive the mathematical relation between refractive indices $n_1$ and $n_2 $ of two radii and radius of curvature R for refraction at a convex spherical surface. Consider the object to be a point since lying on the principle axis in rarer medium of refractive index $n_1$ and a real image formed in the denser medium of refractive index $n_{2}$.Hence, derive lens maker's formula.
    2. Light from a point source in air falls on a convex spherical glass surface of refractive index 1.5 and radius of curvature 20 cm. The distance of light source from the glass surface is 100 cm. At what position is the image formed?
    View Solution
  • 7
    An eye can distinguish between two points of an object if they are separated by more than 0.22mm when the object is placed at 25cm from the eye. The object is now seen by a compound microscope having a 20D objective and 10D eyepiece separated by a distance of 20cm. The final image is formed at 25cm from the eye. What is the minimum separation between two points of the object which can now be distinguished?
    View Solution
  • 8
    1. With the help of a suitable ray diagram, derive the mirror formula for a concave mirror.
    2. The near point of a hypermetropic person is 50 cm from the eye. What is the power of the lens required to enable the person to read clearly a book held at 25 cm from the eye?
    View Solution
  • 9
    Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red, yellow and violet rays are $\mu_\text{r},\mu_\text{y}$ and $\mu_\text{v}$ respectively and those for the flint glass are $\mu'_\text{r},\mu'_\text{y}$ and $\mu'_\text{v}$ respectively. Find the ratio $\frac{\text{A}'}{\text{A}}$ for which.
    1. There is no net angular dispersion.
    2. There is no net deviation in the yellow ray.
    View Solution
  • 10
    Consider a thin lens placed between a source (S) and an observer (O) (Fig). Let the thickness of the lens vary as $\text{w}\text{(b)}=\text{w}_0-\frac{\text{b}^2}{\alpha}$, where b is the verticle distance from the pole. $w_0$ is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.
    View Solution