Question

A bus uses a convex mirror as a viewfinder whose radius of curvature is 4m for metre a car is coming behind the best which is at a distance of 20 metre what will be the position and the size of the image of the car when observed by the driver of the bus through the convex mirror

Answer 1

Explanation:

आप बस यूजेस ऑफ कॉन्वेक्स में एस यू फाइंड रेडियस आफ कर्वेचर इज 4 मीटर आकार इज कमिंग बिहाइंड द बस विच ए डिस्टेंस ऑफ 20 मीटर व्हाट विल बी द पोजीशन एंड साइज ऑफ द इमेज ऑफ द कार व्हेन ऑब्जेक्ट बाय द ड्राइवर ऑल द बेस्ट रोल कॉन्वेक्स मिरर

Answer 2

Answer:

Position: Image is at back side of mirror and at 1.82 m distance.

Size: Image is smaller than object by a factor 0.09.

Explanation:

• Radius of curvature of the mirror, r = 4 m.
• focal length, f = r/2 = 4/2 = 2 m.
• Image distance is v
• Object distance, u = -20m

        (In convex mirror object is placed on the left side of the mirror, so 'u' will be negative)

• From the
• formula of mirror, $\frac{1}{v}$ + $\frac{1}{u}$ = $\frac{1}{f}$

                                                  ⇒  $\frac{1}{v}$  = $\frac{1}{f}$ - $\frac{1}{u}$

                                                  ⇒  $\frac{1}{v}$  = $\frac{1}{2}$ - $\frac{1}{-20}$

                                                  ⇒  $\frac{1}{v}$  = $\frac{1}{2}$ + $\frac{1}{20}$

                                                  ⇒  $\frac{1}{v}$  = $\frac{11}{20}$

                                                  ⇒ v = 20/11 = 1.82 m

• As the image distance is positive , that means image is on the back side of the mirror.
• Now magnification, m = $\frac{height of image}{height of object}$ = - $\frac{v}{u}$

                                    ⇒ m = -$\frac{1.82}{-20}$ = 1.82/20 = 0.09

• Magnification is positive that means image is virtual and erect.
• Magnification less than 1 that means image is smaller than object,
• Conclusion:    (i) The image is formed at back side of mirror and at 1.82 m distance.

         (ii) Image is smaller than object by a factor 0.09.