Answer

Verified

78.3k+ views

**Hint:**The lens that converges rays of light that is parallel to its principal axis. This lens is called a convex lens. The lens that diverges rays of light is called a concave lens. For an object, distance finds the image distance using the lens formula. Now for the new object and image distance the focal length of the concave lens. Then find the focal length of the combination.

**Formula used:**

lens formula:

$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$

**Complete step by step solution:**

The lens converges rays of light that are parallel to its principal axis. This lens is called a convex lens. The lens that diverges rays of light is called a concave lens. The distance between the center of a lens where parallel rays converge or diverge is called the focal length.

When the object is at infinity, the image formed at the focus of the convex lens is real and inverted. When an object is at an imaginary point, then the image will be real, inverted, and of the same size. When an object is at the focal point then the image will be at infinity.

For lenses the sign convention:

The focal length of a convex lens is positive and for a concave lens is negative.

Optical center of a lens lies on the origin of the\[x - y\]axis.

Here it is given that object distance is ${u_1} = - 30cm$, ${f_1} = 10cm$

Then from the lens formula

$\dfrac{1}{v} - \dfrac{1}{{ - 30}} = \dfrac{1}{{10}} \Rightarrow v = 15cm$

Thus, the image is formed at $15cm$ behind the lens.

Here the concave lens of the focal length ${f_2}$ is placed in contact with the convex lens. Hence the screen is shifted by $45cm$ further away.

New image distance ${v_2} = 15 + 45 = 60cm$

Then by using lens formula for combination of lenses

$\Rightarrow$ $\dfrac{1}{{60}} - \dfrac{1}{{ - 30}} = \dfrac{1}{F} \Rightarrow F = 20cm$

Then the focal length of the concave lens

$\Rightarrow$ $\dfrac{1}{F} = \dfrac{1}{{{f_1}}} + \dfrac{1}{{{f_2}}}$

$\Rightarrow$ $\dfrac{1}{{20}} = \dfrac{1}{{10}} + \dfrac{1}{{{f_2}}}$

$\therefore$ ${f_2} = - 20cm$

**Note:**While you're solving problems related to lens, we should take proper care of the signs of different quantities. The focal length of a convex lens is positive and for the concave lens is negative. Optical center of a lens lies on the origin of the \[x - y\] axis. The lens converges rays of light that are parallel to its principal axis.

Recently Updated Pages

Name the scale on which the destructive energy of an class 11 physics JEE_Main

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main

Other Pages

Chloroform reacts with oxygen in the presence of light class 12 chemistry JEE_Main

The voltage of an AC supply varies with time t as V class 12 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main