###### Advertisements

###### Advertisements

A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.

###### Advertisements

#### Solution

Distance between the image (screen) and the object, D = 90 cm

Distance between two locations of the convex lens, d = 20 cm

Focal length of the lens = f

Focal length is related to d and D as:

`"f" = ("D"^2 - "d"^2)/4"D"`

= `((90)^2 - (20)^2)/(4 xx 90)`

= `770/36`

= 21.39 cm

Therefore, the focal length of the convex lens is 21.39 cm.

#### APPEARS IN

#### RELATED QUESTIONS

You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Explain.

A man with normal near point (25 cm) reads a book with small print using a magnifying glass: a thin convex lens of focal length 5 cm.

**(a) **What is the closest and the farthest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass?

**(b)** What is the maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?

A card sheet divided into squares each of size 1 mm^{2} is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 9 cm) held close to the eye.

**(a)** What is the magnification produced by the lens? How much is the area of each square in the virtual image?

**(b)** What is the angular magnification (magnifying power) of the lens?

**(c)** Is the magnification in (a) equal to the magnifying power in (b)? Explain.

An equiconvex lens of focal length '*f*' is cut into two identical plane convex lenses. How will the power of each part be related to the focal length of the original lens ?

A double convex lens of + 5 D is made of glass of refractive index 1.55 with both faces of equal radii of curvature. Find the value of its radius of curvature.

Two concave lenses *L*_{1} and *L*_{2} are kept in contact with each other. If the space between the two lenses is filled with a material of smaller refractive index, the magnitude of the focal length of the combination

Two converging lenses of unequal focal lengths can be used to reduce the aperture of a parallel beam of light without loosing the energy of the light. This increase the intensity. Describe how the converging lenses should be placed to do this.

A convex lens forms a real image of a point object placed on its principals axis. If the upper half of the lens is painted black,

(a) the image will be shifted downward

(b) the image will be shifted upward

(c) the image will not be shifted

(d) the intensity of the image will decrease.

A small piece of wood is floating on the surface of a 2.5 m deep lake. Where does the shadow form on the bottom when the sum is just setting? Refractive index of water = 4/3.

A pin of length 2.0 cm lies along the principal axis of a converging lens, the centre being at a distance of 11 cm from the lens. The focal length of the lens is 6 cm. Find the size of the image.

An object approaches a convergent lens from the left of the lens with a uniform speed 5 m/s and stops at the focus. The image ______.

A plano convex lens has diameter of 10 cm and its thickness at the centre is 0.5 cm. Speed of light in the lens is 2 × 10^{8} ms^{-1}. What is the focal length of the lens?

Show that the least possible distance between an object and its real image in a convex lens is 4f, where f is the focal length of the lens.